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Topic: Nine papers and a monograph published by Geometry & Topology Publications
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Geometry and Topology

Posts: 140
Registered: 5/24/06
Nine papers and a monograph published by Geometry & Topology Publications
Posted: Jun 22, 2013 8:54 AM
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The on-line version of Geometry & Topology Monographs Volume 18:  

         Proceedings of the Freedman Fest
         ================================
Editors: Rob Kirby, Vyacheslav Krushkal and Zhenghan Wang

is now complete at:   http://msp.warwick.ac.uk/gtm/2012/18/


Four papers have been published by Algebraic & Geometric Topology

(1) Algebraic & Geometric Topology 13 (2013) 2207-2238
   Cohomology of Kac-Moody  groups over a finite field
     by Jaume Aguade and Albert Ruiz
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-04/p070.xhtml
   DOI: 10.2140/agt.2013.13.2207

(2) Algebraic & Geometric Topology 13 (2013) 2239-2260
   The absolute gradings on embedded contact homology   
   and Seiberg-Witten Floer cohomology
     by Daniel Cristofaro-Gardiner
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-04/p071.xhtml
   DOI: 10.2140/agt.2013.13.2239

(3) Algebraic & Geometric Topology 13 (2013) 2261-2282
   Embedding relatively hyperbolic groups in products of trees
     by John M Mackay and Alessandro Sisto
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-04/p072.xhtml
   DOI: 10.2140/agt.2013.13.2261

(4) Algebraic & Geometric Topology 13 (2013) 2283-2316
   A finite-dimensional approach to the strong Novikov conjecture
     by Daniel Ramras, Rufus Willett and Guoliang Yu
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-04/p073.xhtml
   DOI: 10.2140/agt.2013.13.2283

Five papers have been published by Geometry & Topology

(5) Geometry & Topology 17 (2013) 1497-1534
   Intersections of quadrics, moment-angle manifolds and connected sums
     by Samuel Gitler and Santiago Lopez de Medrano
   URL: http://www.msp.warwick.ac.uk/gt/2013/17-03/p034.xhtml
   DOI: 10.2140/gt.2013.17.1497

(6) Geometry & Topology 17 (2013) 1535-1579
   Lipschitz retraction and distortion for subgroups of Out(F_n)
     by Michael Handel and Lee Mosher
   URL: http://www.msp.warwick.ac.uk/gt/2013/17-03/p035.xhtml
   DOI: 10.2140/gt.2013.17.1535

(7) Geometry & Topology 17 (2013) 1581-1670
   The free splitting complex of a free group, I: hyperbolicity
     by Michael Handel and Lee Mosher
   URL: http://www.msp.warwick.ac.uk/gt/2013/17-03/p036.xhtml
   DOI: 10.2140/gt.2013.17.1581

(8) Geometry & Topology 17 (2013) 1671-1706
   Motivic Brown-Peterson invariants of the rationals
     by Kyle M Ormsby and Paul Arne Ostvaer
   URL: http://www.msp.warwick.ac.uk/gt/2013/17-03/p037.xhtml
   DOI: 10.2140/gt.2013.17.1671

(9) Geometry & Topology 17 (2013) 1707-1744
   Random rigidity in the free group
     by Danny Calegari and Alden Walker
   URL: http://www.msp.warwick.ac.uk/gt/2013/17-03/p038.xhtml
   DOI: 10.2140/gt.2013.17.1707

Abstracts follow

(1) Cohomology of Kac-Moody  groups over a finite field
     by Jaume Aguade and Albert Ruiz

We compute the mod p cohomology algebra of a family of infinite
discrete Kac-Moody groups of rank two defined over finite fields of
characteristic different from p.


(2) The absolute gradings on embedded contact homology   
   and Seiberg-Witten Floer cohomology
     by Daniel Cristofaro-Gardiner

Let Y be a closed connected contact 3-manifold.  In [Geom. Topol. 14
(2010) 2497-2581], Taubes defines an isomorphism between the
embedded contact homology (ECH) of Y and its Seiberg-Witten Floer
cohomology.  Both the ECH of Y and the Seiberg-Witten Floer cohomology
of Y admit absolute gradings by homotopy classes of oriented 2-plane
fields.  We show that Taubes' isomorphism preserves these gradings,
which implies that the absolute grading on ECH is a topological
invariant.  To do this, we prove another result relating the expected
dimension of any component of the Seiberg-Witten moduli space over a
completed connected symplectic cobordism to the ECH index of a
corresponding homology class.


(3) Embedding relatively hyperbolic groups in products of trees
     by John M Mackay and Alessandro Sisto

We show that a relatively hyperbolic group quasi-isometrically embeds
in a product of finitely many trees if the peripheral subgroups do,
and we provide an estimate on the minimal number of trees needed.
Applying our result to the case of 3-manifolds, we show that
fundamental groups of closed 3-manifolds have linearly controlled
asymptotic dimension at most 8.  To complement this result, we observe
that fundamental groups of Haken 3-manifolds with non-empty boundary
have asymptotic dimension 2.


(4) A finite-dimensional approach to the strong Novikov conjecture
     by Daniel Ramras, Rufus Willett and Guoliang Yu

The aim of this paper is to describe an approach to the (strong)
Novikov conjecture based on continuous families of finite-dimensional
representations: this is partly inspired by ideas of Lusztig related
to the Atiyah-Singer families index theorem, and partly by Carlsson's
deformation K-theory.  Using this approach, we give new proofs of the
strong Novikov conjecture in several interesting cases, including
crystallographic groups and surface groups.  The method presented here
is relatively accessible compared with other proofs of the Novikov
conjecture, and also yields some information about the K-theory and
cohomology of representation spaces.


(5) Intersections of quadrics, moment-angle manifolds and connected sums
     by Samuel Gitler and Santiago Lopez de Medrano

For the intersections of real quadrics in R^n and in C^n associated to
simple polytopes (also known as universal abelian covers and
moment-angle manifolds, respectively) we obtain the following results:
(1) Every such manifold of dimension greater than or equal to 5,
connected
up to the middle dimension and with free homology is diffeomorphic to a
connected sum of sphere products. The same is true for the manifolds in
infinite
families stemming from each of them. This includes the moment-angle
manifolds
for which he result was conjectured by F Bosio and L Meersseman.
(2) The topological effect on the manifolds of cutting off vertices and
edges
from the polytope is described. Combined with the result in (1), this
gives
the same result for many more natural, infinite families.
(3) As a consequence of (2), the cohomology rings of the two manifolds
associated to a polytope need not be isomorphic, contradicting published
results about complements of arrangements.
(4) Auxiliary but general constructions and results in Geometric
Topology.


(6) Lipschitz retraction and distortion for subgroups of Out(F_n)
     by Michael Handel and Lee Mosher

Given a free factor A of the rank n free group F_n, we characterize
when the subgroup of Out(F_n) that stabilizes the conjugacy class of A
is distorted in Out(F_n). We also prove that the image of the natural
embedding of Aut(F_{n-1}) in Aut(F_n) is nondistorted, that the
stabilizer in Out(F_n) of the conjugacy class of any free splitting of
F_n is nondistorted and we characterize when the stabilizer of the
conjugacy class of an arbitrary free factor system of F_n is
distorted. In all proofs of nondistortion, we prove the stronger
statement that the subgroup in question is a Lipschitz retract. As
applications we determine Dehn functions and automaticity for Out(F_n)
and Aut(F_n).


(7) The free splitting complex of a free group, I: hyperbolicity
     by Michael Handel and Lee Mosher

We prove that the free splitting complex of a finite rank free group,
also known as Hatcher's sphere complex, is hyperbolic.


(8) Motivic Brown-Peterson invariants of the rationals
     by Kyle M Ormsby and Paul Arne Ostvaer

Let BP<n>, n at least 0 and at most infinity, denote the family of
motivic truncated Brown-Peterson spectra over Q.  We employ a
`local-to-global' philosophy in order to compute the bigraded homotopy
groups of BP<n>.  Along the way, we produce a computation of the
homotopy groups of BP<n> over Q_2, prove a motivic Hasse principle for
the spectra BP<n>, and reprove several classical and recent theorems
about the K-theory of particular fields in a streamlined fashion.  We
also compute the bigraded homotopy groups of the 2-complete algebraic
cobordism spectrum MGL over Q.


(9) Random rigidity in the free group
     by Danny Calegari and Alden Walker

We prove a rigidity theorem for the geometry of the unit ball in
random subspaces of the scl norm in B_1^H of a free group. In a free
group F of rank k, a random word w of length n (conditioned to lie in
[F,F]) has scl(w) = log(2k-1)n / 6 log(n) + o(n / log(n)) with high
probability, and the unit ball in a subspace spanned by d random words
of length O(n) is C^0 close to a (suitably affinely scaled)
octahedron.
A conjectural generalization to hyperbolic groups and manifolds
(discussed in the appendix) would show that the length of a random
geodesic in a hyperbolic manifold can be recovered from the bounded
cohomology of the fundamental group.



  Geometry & Topology Publications is an imprint of
  Mathematical Sciences Publishers



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