Math Forum Discussions

Jean-Claude Evard

Posts: 30
Registered: 12/13/04

Some references on the new historical event
Posted: Jun 14, 2006 6:08 PM

Plain Text

The purpose of this posting is to collect important references on the
recent historical event in mathematics. While the collection below is
far to be complete, it can already save a lot time to anyone
interested in the classification of 3-manifolds.

This posting contains the following parts:

1. The new historical event
2. The two papers containing the last step.
3. Previous work.
3.1 Historical publications of William Thurston.
3.2 Historical publications of Richard Hamilton.
3.3 Historical publications of Grisha Perelman.
4. Related books.
5. Related papers.
6. Online publications and comments.
7. Talks presented by the main contributors.
8. About the main contributors.
9. Threads posted on the internet about the historical event.
10. Online comments about the historical event from universities
and newspapers.
===============================================
1. The new historical event

Many mathematicians already know the recent historical news
that the last step of the proof of the Thurston's geometrization
conjecture, and its special case, Poincaré?s conjecture, has just
been published.

This news was first announced by Sun Yat-sen University
on June 3, 2006:
http://www.sysu.edu.cn/en/2006news/0603.htm
It was first announced on sci.math by Edwin Clark,
on the following thread, started on June 4, 2006, at 8:15 AM:
http://mathforum.org/kb/thread.jspa?threadID=1392801&tstart=15

It is amazing that such a huge historical event happens only
two years after 2004, when the last step of the proof of the
Catalan conjecture was published, only seven years after 1999,
when the last step of the proof of the Shimura-Taniyama conjecture
was published, and only eleven years after 1995, when the last step
of the proof of Fermat`s Last Theorem was published.
===============================================
2. The two papers containing the last step.

The last step of the proof of Thurston's geometrization conjecture,
and Poincare`s conjecture as a special case, has been published in
the following two concurrent papers:

First paper containing the last step:

Huai-Dong Cao and Xi-Ping Zhu,
A Complete Proof of the Poincaré and Geometrization Conjectures -
application of the Hamilton-Perelman theory of the Ricci flow,
Asian Journal of Mathematics, Volume 10, Number 2, pages 165-498,
June 2006,
http://www.intlpress.com/AJM/p/2006/10_2/AJM-10-2-165-498-Abstract.php

Abstract: In this paper, we give a complete proof of the Poincaré
and the geometrization conjectures. This work depends on the
accumulative works of many geometric analysts in the past thirty
years. This proof should be considered as the crowning achievement
of the Hamilton-Perelman theory of Ricci flow.

Second paper containing the last step:

Notes and commentary on Perelman's Ricci flow papers
Bruce Kleiner and John Lott
at the University of Michigan
http://www.math.lsa.umich.edu/~lott/ricciflow/perelman.html
===============================================
3. Previous work.

Before this last step, a huge amount of work has been achieved
by many other famous mathematicians, notably William Thurston,
Richard Hamilton, and Grisha Perelman.

Here are some key references to their work:
===============================================
3.1 Historical publications of William Thurston:

The Geometry and Topology of Three-Manifolds
by William P. Thurston
Electronic edition of the 1980 notes distributed by Princeton University.
http://www.msri.org/publications/books/gt3m/

The following book is a considerable expansion of the first few
chapters of these notes. Later
chapters have not yet appeared in book form:

William Thurston,
Three-dimensional geometry and topology. Vol. 1.
Edited by Silvio Levy. Princeton Mathematical Series, 35.
Princeton University Press, Princeton, NJ, 1997. x+311 pp.
http://www.pupress.princeton.edu/titles/6086.html
William Thurston was awarded the 2005 AMS-Book prize for this book:
http://www.ams.org/ams/press/book-thurston.html
See also the Notices of the AMS, Volume 52, Number 4,
page 450, April 2005:
http://www.ams.org/notices/200504/comm-book.pdf

===============================================
3.2 Historical publications of Richard Hamilton:

The main tool of the proof of Thurston's geometrization conjecture
is the Ricci flow. This tool was created by Richard Hamilton, and
published in the following historical paper:

Richard Hamilton,
Three-manifolds with positive Ricci curvature,
J. Differential Geom. 17, no. 2, 255--306, 1982.

This key paper is included in the following book:

Collected papers on Ricci flow.
Edited by H. D. Cao, B. Chow, S. C. Chu and S. T. Yau.
Series in Geometry and Topology, 37.
International Press, Somerville, MA, 2003. viii+545 pp.
ISBN: 1-57146-110-8
Mathematical Review Number: MR2145154 (2006e:53002)
AMS 2000 Mathematics subject classification
numbers: 53-06 (53C21 53C44)
Description by the publisher at the Web address:
http://www.intlpress.com/books/RicciFlow.php
===============================================
3.3 Historical publications of Grisha Perelman

Grisha Perelman.
The entropy formula for the Ricci flow and its geometric applications,
First version: November 11, 2002, 39 pages
Most recent version: May 21, 2006, 39 pages
http://arxiv.org/abs/math.DG/0211159

Grisha Perelman,
Ricci flow with surgery on three-manifolds,
First version: March 10, 2003, 22 pages
Most recent version: May 21, 2006, 22 pages
http://arxiv.org/abs/math.DG/0303109

Grisha Perelman,
Finite extinction time for the solutions to the Ricci flow
on certain three-manifolds,
First version: July 17, 2003, 7 pages
Most recent version: May 21, 2006, 7 pages
math.DG/0307245
http://arxiv.org/abs/math.DG/0307245
===============================================
4. Related books

Bennett Chow and Dan Knopf,
The Ricci flow: an introduction,
Mathematical Surveys and Monographs, 110,
American Mathematical Society, Providence, RI, 2004.
xii+325 pp.
ISBN 0-8218-3515-7
Mathematical Review number: MR2061425 (2005e:53101)
AMS 2000 Mathematics subject classification
numbers: 53C44 (35K60 53C21)

John Hempel,
3-manifolds,
Reprint of the 1976 original,
AMS Chelsea Publishing, Providence, RI, 2004.
xii+195 pp.
ISBN 0-8218-3695-1
Mathematical Review number: MR2098385 (2005e:57053)
AMS 2000 Mathematics subject classification
number: 57N10

William Jaco and Peter Shalen,
Seifert fibered spaces in 3-manifolds,
Mem. Amer. Math. Soc. 21 (1979), no. 220, viii+192 pp.
Mathematical Review number: MR0539411 (81c:57010)
AMS 2000 Mathematics subject classification
number: 57N10

Klaus Johannson,
Homotopy equivalences of 3-manifolds with boundaries,
Lecture Notes in Mathematics, 761,
Springer, Berlin, 1979. ii+303 pp.
ISBN 3-540-09714-7
Mathematical Review number: MR0551744 (82c:57005)
AMS 2000 Mathematics subject classification
number: 57N10

Klaus Johannson,
Topology and combinatorics of 3-manifolds,
Lecture Notes in Mathematics, 1599,
Springer-Verlag, Berlin, 1995. xviii+446 pp.
ISBN 3-540-59063-3
Mathematical Review number: MR1439249 (98c:57014)
AMS 2000 Mathematics subject classification
numbers: 57N10 (57M50)

William Thurston,
Three-dimensional geometry and topology. Vol. 1,
Edited by Silvio Levy. Princeton Mathematical Series, 35,
Princeton University Press, Princeton, NJ, 1997. x+311 pp.
http://www.pupress.princeton.edu/titles/6086.html
William Thurston was awarded the 2005 AMS-Book prize for this book:
http://www.ams.org/ams/press/book-thurston.html
See also the Notices of the AMS, Volume 52, Number 4,
page 450, April 2005:
http://www.ams.org/notices/200504/comm-book.pdf

Lectures on the Ricci flow
Peter Topping
March 9, 2006
Posted on the internet at the address
http://www.maths.warwick.ac.uk/~topping/RFnotes.html
Series: London Mathematical Society Lecture Note Series (No. 325)
Paperback (ISBN-13: 9780521689472 | ISBN-10: 0521689473)
Not yet published - available from August 2006
===============================================
5. Related papers.

Collected papers on Ricci flow.
Edited by H. D. Cao, B. Chow, S. C. Chu and S. T. Yau.
Series in Geometry and Topology, 37.
International Press, Somerville, MA, 2003. viii+545 pp.
ISBN: 1-57146-110-8
Mathematical Review Number: MR2145154 (2006e:53002)
AMS 2000 Mathematics subject classification
numbers: 53-06 (53C21 53C44)

Robert Greene,
Some recent developments in Riemannian geometry,
pages 1--30 from:
Recent developments in geometry,
Proceedings of the AMS Special Session on Geometry,
held at the University of California, Los Angeles,
November 14--15, 1987,
Edited by S.-Y. Cheng, H. Choi and Robert E. Greene,
Contemporary Mathematics, 101,
American Mathematical Society, Providence, RI, 1989,
xiv+338 pp.
ISBN 0-8218-5107-1
Mathematical Review Number: MR1034969 (91b:53044)
AMS 2000 Mathematics subject classification
number: 53C20

The following paper was the first paper published by William Hake.
It contains key ideas leading to the concept of Haken 3-manifold.
More information about this can be found in the paper of William
Jaco and Ulrich Oertel published in 1984.

Wolfgang Haken,
Theorie der Normalflächen. (German),
Acta Math. 105 1961 245--375.
Mathematical Review Number: MR0141106 (25 #4519a)
AMS 2000 Mathematics subject classification
numbers: 55.20 (55.60)

The following paper is the historical paper
where the Ricci flow was created:

Hamilton, Richard.
Three-manifolds with positive Ricci curvature.
J. Differential Geom. 17 (1982), no. 2, 255--306.
Mathematical Review Number: MR0664497 (84a:53050)
AMS 2000 Mathematics subject classification
numbers: 53C25 (35K55 58G30)

Richard Hamilton has published about 35 papers after his above
historical paper.

William Jaco and Ulrich Oertel,
An algorithm to decide if a $3$-manifold is a Haken manifold,
Topology 23 (1984), no. 2, 195--209.
Mathematical Review Number: MR0744850 (85j:57014)
AMS 2000 Mathematics subject classification
number: 57N10

Jean-Pierre Otal,
Thurston's hyperbolization of Haken manifolds,
Surveys in differential geometry, Vol. III
(Cambridge, MA, 1996), 77--194,
Int. Press, Boston, MA, 1998.
Mathematical Review Number: MR1677888 (2000b:57025))
AMS 2000 Mathematics subject classification
number: 57M50

The following paper is the historical paper where William Thurston
introduced his geometrization conjecture, and proved that it is true
in the special case of Haken 3-manifolds:

William Thurston,
Hyperbolic geometry and 3-manifolds,
Low-dimensional topology (Bangor, 1979), pp. 9--25,
London Math. Soc. Lecture Note Ser., 48,
Cambridge Univ. Press, Cambridge-New York, 1982.
57N10 (30F40 53A40)
Mathematical Review Number: MR0662424 (83j:57006)
AMS 2000 Mathematics subject classification
numbers: 57N10 (30F40 53A40)

William Thurston has published about 40 papers after the above
historical paper.

The following paper is a historical paper about a large class
of 3-manifolds that they are topologically characterized by
their fundamental groups:

Friedhelm Waldhausen,
On irreducible 3-manifolds which are sufficiently large,
Ann. of Math. (2) 87 1968: 56--88,
Mathematical Review Number: MR0224099 (36 #7146)
AMS 2000 Mathematics subject classification
number: 57.05
===============================================
6. Online publications and comments.

The main Web site of information about the Ricci flow is the following:
Notes and commentary on Perelman's Ricci flow papers,
Web site maintained
by Bruce Kleiner at Yale University
and John Lott at the University of Michigan in Ann Arbor:
http://www.math.lsa.umich.edu/~lott/ricciflow/perelman.html

Additional online publications and comments:

Remarks on Perelman?s papers
by Michael Anderson,
13 pages, July 30, 2003,
http://www.math.sunysb.edu/~anderson/perelman.pdf

Michael Anderson,
Geometrization of 3-Manifolds via the Ricci Flow,
Notices of the American Mathematical Society,
Volume 51, Number 2, pp. 184--193, February 2004
http://www.ams.org/notices/200402/fea-anderson.pdf

Michael Anderson,
Singularities of the Ricci flow,
9 pages, June 2005,
to appear in Encyclopedia of Mathematical Physics, Elsevier,
http://www.math.sunysb.edu/~anderson/ricciflow.pdf

Huai-Dong Cao and Richard Hamilton,
Gradient Kahler-Ricci Solitons and Periodic Orbits,
12 pages, July 2, 1998,
to appear in Comm. Anal. Geom.:
http://arxiv.org/abs/math.DG/9807009

Huai-Dong Cao and Bennett Chow,
Recent Developments on the Ricci Flow
Research report, 22 pages, November 20, 1998,
http://arxiv.org/abs/math.DG/9811123

Huai-dong Cao and Lei Ni,
Matrix Li-Yau-Hamilton estimates for the heat equation
on Kaehler manifolds,
11 pages, August 2002, posted on November 18, 2002:
http://arxiv.org/abs/math.DG/0211283

Huai-Dong Cao, Bing-Long Chen, and Xi-Ping Zhu,
Ricci flow on compact Kähler manifolds
of positive bisectional curvature,
4 pages, February 8, 2003,
http://arxiv.org/abs/math.DG/0302087
http://front.math.ucdavis.edu/math.DG/0302087

Bing-Long Chen and Xi-Ping Zhu,
Ricci Flow with Surgery on Four-manifolds
with Positive Isotropic Curvature,
Version 1: April 23, 2005, 105 pages.
Version 2: May 30, 2005, 84 pages.
Version 3: June 4, 2006, 68kb, 105 pages.
http://arxiv.org/abs/math.DG/0504478

Panagiota Daskalopoulos and Natasa Sesum,
Eternal Solutions to the Ricci Flow on R^2,
Version 1: March 22, 2006,
Version 2: March 23, 2006,
AMS 2000 Mathematics subject classification numbers: 35J60
http://arxiv.org/abs/math/0603525

Review by Robert Greene published in the
Bulletin of the American Mathematical Society,
Volume 35, Number 2, April 1998, Pages 179--188,
and posted on the internet at the address:
http://www.ams.org/bull/1998-35-02/S0273-0979-98-00748-4/
S0273-0979-98-00748-4.pdf
of the book:
William Thurston,
Three-dimensional geometry and topology. Vol. 1.
Edited by Silvio Levy. Princeton Mathematical Series, 35.
Princeton University Press, Princeton, NJ, 1997. x+311 pp.

Biography of Jules Henri Poincare,
by Yann Lamontagne, November 6, 2005,
http://planetmath.org/encyclopedia/JulesHenriPoincare.html
Yann Lamontagne:
http://planetmath.org/?op=getuser&id=40

John Milnor
The Poincare Conjecture 99 Years Later: A Progress Report
8 pages, 2003:
http://www.math.sunysb.edu/~jack/PREPRINTS/poiproof.pdf
The Poincare Conjecture One Hundred Years Later,
8 pages, 2004:
http://www.math.sunysb.edu/~jack/PREPRINTS/poi-04a.pdf

John Milnor,
Towards the Poincare Conjecture and the Classification of 3-Manifolds,
Preprint of June 14, 2003, 12 pages:
http://www.math.sunysb.edu/~jack/PREPRINTS/tpc.pdf
Final version:
Notices of the AMS, Volume 50, Number 10,
pp. 1226--1233, November 2003,
http://www.ams.org/notices/200310/fea-milnor.pdf

John Morgan,
Recent progress on the Poincare conjecture and the classification
of 3-manifolds,
Bulletin of the American Mathematical Society,
Volume 42, Number 1, Pages 57?78
Article electronically published on October 29, 2004
http://www.ams.org/bull/2005-42-01/
S0273-0979-04-01045-6/S0273-0979-04-01045-6.pdf

Description of Thurston's geometrization conjecture
on e-Paranoids:
http://www.e-paranoids.com/t/th/thurston_conjecture.html

Zhongmin Qian,
Ricci flow on a 3-manifold with positive scalar curvature I,
Mathematical Institute, University of Oxford
December 2003,
http://www.maths.ox.ac.uk/~qianz/_private/qianric1newox.pdf

Comments on Grigory Perelman?s papers:
Perelman and the Poincare Conjecture,
posted by Peter Woit,
on September 8, 2004,
with 17 responses:
http://www.math.columbia.edu/~woit/wordpress/?p=77
Web site of Peter Woit at Columbia University:
http://www.math.columbia.edu/~woit/
===============================================
7. Talks presented by the main contributors.

April 21 ? May 2, 2003
Grigory Perelman
Steklov Institute St. Petersburg, Russia
Ricci Flow and the Geometrization of 3-Manifolds
Stony Brook University
http://www.math.sunysb.edu/events/grisha/poster.pdf

July 1 to July 21, 2004,
International Summer School on Analysis
Hangzhou-Beijing, China
Related talks:
Bennett Chow, University of California at San Diego:
Ricci Flow and recent Developments
Xiping Zhu. Zhongshan University:
Ancient Solutions of the Ricci Flows,
http://cms.zju.edu.cn/Econferencesystem/analysis/poster.htm

May 15-17, 2005,
Workshop on Flows in Geometry,
Harvard University,
Organizers:
Huai-Dong Cao, Lehigh University,
Panagiota Daskalopoulos, Columbia University,
Richard Hamilton, Columbia University,
Shing-Tung Yau, Harvard University.
Talks related to the Ricci flow:
Natasa Sesum, New York University,
A compactness theorem for Kähler-Ricci solitons,
Albert Chau, Harvard University,
On the uniformization of complete Kähler manifolds
with nonnegative curvature,
Huai-Dong Cao, Lehigh University,
Second variation of Perelman's functionals and stability for Ricci solitons,
Xi-Ping Zhu, Zhongshan University, China,
Uniqueness of the Ricci flow on complete noncompact manifolds,
David Jerison, Massachusetts Institute of Technology,
An informal discussion of Perelman's work,
Ben Weinkove, Harvard University,
Moment map flows and Kahler geometry,
http://www.math.harvard.edu/jdg/fig.html

March 4-5, 2006
Workshop on Geometric Flows
Harvard University,
Organizers:
Huai-Dong Cao, Lehigh University,
Panagiota Daskalopoulos, Columbia University,
Richard Hamilton, Columbia University,
Shing-Tung Yau, Harvard University.
Talks related to the Ricci flow:
Lei Ni, University of California at San Diego,
Local monotonicity and regularity for Ricci flow,
Natasa Sesum, Columbia University,
The Kähler Ricci flow and properties of the solutions
of the conjugate heat equation
Xi-Ping Zhu (Zhongshan visiting Harvard):
Uniqueness of the Ricci flow on complete non-compact manifolds
http://www.math.harvard.edu/ricci/ricci.pdf

June 19---24, 2006,
International conference on string theory in Beijing,
http://strings06.itp.ac.cn/
http://strings06.itp.ac.cn/?id=international
http://english.gov.cn/2006-05/26/content_291612.htm
It said in China View of June 4, 2006,
http://news.xinhuanet.com/english/2006-06/04/content_4644754.htm
that Shing-Tung Yau from Harvard University will himself
explain the methodology of proving the Poincare Conjecture
at the 2006 International Conference on String Theory.
===============================================
8. About the main contributors.

Michael Anderson is Faculty member of the Department of Mathematics
of the State University of New York at Stony Brook:
http://www.math.sunysb.edu/~anderson/

Huai-Dong Cao is Faculty member of the Department of Mathematics
of Lehigh University:
http://www.lehigh.edu/~huc2/

Bennett Chow is Faculty member of the Department of Mathematics
of the University of California at San Diego:
http://www.math.ucsd.edu/~benchow/

Robert Greene is Faculty member of the Department of Mathematics
of the University of California at Los Angeles:
http://www.math.ucla.edu/~greene/

Richard Hamilton is Faculty member of the Department of Mathematics
of Columbia University:
http://www.math.columbia.edu/people/faculty.phtml

John Hempel is Faculty member of the Departments of Mathematics
of Rice University:
http://math.rice.edu/~hempel/

William Jaco is Faculty member of the Departments of Mathematics
of Oklahoma State University:
http://www.math.okstate.edu/~jaco/

Bruce Kleiner is Faculty member of the Departments of Mathematics
of the University of Michigan:
http://www.math.lsa.umich.edu/people/facultyDetail.php?id=223
and of Yale University:
http://www.math.yale.edu/~bk255/

Daniel Knopf is Faculty member of the Department of Mathematics
of the University of Texas at Austin:
http://www.ma.utexas.edu/users/danknopf/

John Lott is Faculty member of the Department of Mathematics
of the University of Michigan:
http://www.math.lsa.umich.edu/~lott/

John Milnor is Director of the Institute for Mathematical Sciences
of the State University of New York at Stony Brook:
http://www.math.sunysb.edu/~jack/

Lei Ni is Faculty member of the Department of Mathematics
of the University of California at San Diego:
http://www.math.ucsd.edu/~lni/

Grigory Perelman is Faculty member of the Laboratory
of Mathematical Physics of Steklov Institute of Mathematics
in St.Petersburg, Russia:
http://www.pdmi.ras.ru/staff/perelman.html

Zhongmin Qian is Faculty member of the Mathematical Institute
of the University of Oxford
http://www.maths.ox.ac.uk/~qianz/

Natasa Sesum is Faculty member of the Department of Mathematics
of Columbia University
http://www.math.columbia.edu/~natasas/

Peter B. Shalen is Faculty member of the Department of Mathematics,
Statistics, and Computer Science, of the University of Illinois at Chicago:
http://www.math.uic.edu/~shalen/

William Thurston is Faculty member of the Department of Mathematics
of Cornell University:
http://www.math.cornell.edu/People/Faculty/thurston.html
The Fields Medal was awarded to William Thurston in 1982,
notably for his proof of the geometrization conjecture in the
special case of Haken manifolds:
http://www.mathunion.org/medals/Fields/Prizewinners.html
William Thurston was awarded the 2005 AMS-Book prize
for his book Three-dimensional geometry and topology:
http://www.ams.org/ams/press/book-thurston.html
See also the Notices of the AMS, Volume 52, Number 4,
page 450, April 2005:
http://www.ams.org/notices/200504/comm-book.pdf

Peter Topping is Faculty member of the Mathematics Institute
of the University of Warwick in the United Kingdom:
http://www.maths.warwick.ac.uk/~topping/

Friedhelm Waldhausen is Emeriti Faculty member of the
Fakultät für Mathematik der Universität Bielefeld in Germany:
http://www.mathematik.uni-bielefeld.de/

Shing-Tung Yau is Faculty member
of the Department of Mathematics of Harvard University:
http://www.math.harvard.edu/people/YauShing-Tung.html
He is Editor-In-Chief of the Asian Journal of Mathematics,
http://www.ims.cuhk.edu.hk/~ajm/
where the historical paper of Huai-Dong Cao and Xi-Ping Zhu
will be published this month.
The Fields Medal was awarded to Shing-Tung Yau in 1982:
http://www.mathunion.org/medals/Fields/Prizewinners.html

Xiping Zhu is Faculty member of the Department of Mathematics
of Sun Yat-sen University in China:
http://www.sysu.edu.cn/en/privilegedscholars.htm
===============================================
9. Threads posted on the internet about the historical event.

The first thread was started by Edwin Clark on sci.math,
on June 4, 2006, at 8:15 AM:
http://mathforum.org/kb/thread.jspa?threadID=1392801&tstart=15

The second thread was started by Yao Ziyuan on sci.math,research
on June 4, 2006, at 10:30 AM
http://mathforum.org/kb/thread.jspa?threadID=1392841&tstart=0

The third thread was started by Yao Ziyuan on sci.math
on June 5, 2006, at 3:02 AM
http://mathforum.org/kb/thread.jspa?threadID=1393187&tstart=0

The fourth thread was started by Yao on geometry.research
on June 5, 2006, at 3:45 AM
http://mathforum.org/kb/thread.jspa?threadID=1393204&tstart=0

The fifh thread was started by V.Z. Nuri on sci.math
on June 8, 2006, at 10:12 PM
http://mathforum.org/kb/thread.jspa?threadID=1395340&tstart=30
===============================================
10. Comments from universities and newspapers.

June 3, 2006,
announcement of the historical event
by Sun Yat-sen University Guangzhou, P.R. China
http://www.sysu.edu.cn/en/2006news/0603.htm

June 4, 2006,
announcement of the historical event in China View:
http://news.xinhuanet.com/english/2006-06/04/content_4644754.htm
It contains the following piece of information:
Zhu and Cao were invited last September by the Harvard
Mathematics Department to conduct academic exchange at Harvard.
In the following half year, they spent three hours every week
to explain their work to five Harvard mathematicians.

June 4th, 2006,
announcement of the historical event in India eNews.com:
http://indiaenews.com/2006-06/10242-solving-toughest-
puzzle-outstanding-job-chinese-mathematician.htm

June 05, 2006,
announcement of the historical event in the People?s Daily Online:
Chinese mathematicians put final pieces in global puzzle:
http://english.people.com.cn/200606/04/eng20060604_270860.html

June 6 2006,
announcement of the historical event in the Guardian Unlimited;
Has Poincare's Conjecture been solved? The conjecture continues.
By Charles Arthur:
http://blogs.guardian.co.uk/technology/archives/2006/06/06/has_poincares_
conjecture_been_solved_the_conjecture_continues.html
===============================================
With best regards,

Jean-Claude Evard
Western Kentucky University
Department of Mathematics
E-mail: Jean-Claude.Evard@wku.edu