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Ten papers published by Geometry & Topology Publications
Posted:
Sep 26, 2011 10:30 AM
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Nine papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 2453-2475
The Goodwillie tower for S^1 and Kuhn's Theorem
by Mark Behrens
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p080.xhtml
DOI: 10.2140/agt.2011.11.2453
(2) Algebraic & Geometric Topology 11 (2011) 2477-2545
Real homotopy theory of semi-algebraic sets
by Robert Hardt, Pascal Lambrechts, Victor Turchin and Ismar Volic
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p081.xhtml
DOI: 10.2140/agt.2011.11.2477
(3) Algebraic & Geometric Topology 11 (2011) 2547-2578
The cactus tree of a metric space
by Panos Papasoglu and Eric Swenson
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p082.xhtml
DOI: 10.2140/agt.2011.11.2547
(4) Algebraic & Geometric Topology 11 (2011) 2579-2585
More on the anti-automorphism of the Steenrod algebra
by Vince Giambalvo and Haynes R Miller
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p083.xhtml
DOI: 10.2140/agt.2011.11.2579
(5) Algebraic & Geometric Topology 11 (2011) 2587-2625
Z-Structures on product groups
by Carrie J Tirel
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p084.xhtml
DOI: 10.2140/agt.2011.11.2587
(6) Algebraic & Geometric Topology 11 (2011) 2627-2653
Paires de structures de contact sur les varietes de dimension trois
by Vincent Colin and Sebastiao Firmo
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p085.xhtml
DOI: 10.2140/agt.2011.11.2627
(7) Algebraic & Geometric Topology 11 (2011) 2655-2679
Topological classification of torus manifolds which have
codimension one extended actions
by Suyoung Choi and Shintaro Kuroki
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p086.xhtml
DOI: 10.2140/agt.2011.11.2655
(8) Algebraic & Geometric Topology 11 (2011) 2681-2739
Sutured Floer homology, sutured TQFT and noncommutative QFT
by Daniel V Mathews
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p087.xhtml
DOI: 10.2140/agt.2011.11.2681
(9) Algebraic & Geometric Topology 11 (2011) 2741-2774
Studying uniform thickness II: Transversely nonsimple iterated torus knots
by Douglas J LaFountain
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p088.xhtml
DOI: 10.2140/agt.2011.11.2741
One paper has been published by Geometry & Topology
(10) Geometry & Topology 15 (2011) 1569-1615
Quantum traces for representations of surface groups in SL_2(C)
by Francis Bonahon and Helen Wong
URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p040.xhtml
DOI: 10.2140/gt.2011.15.1569
Abstracts follow
(1) The Goodwillie tower for S^1 and Kuhn's Theorem
by Mark Behrens
We analyze the homological behavior of the attaching maps in the
2-local Goodwillie tower of the identity evaluated at S^1. We show
that they exhibit the same homological behavior as the James-Hopf maps
used by N Kuhn to prove the 2-primary Whitehead conjecture. We use
this to prove a calculus form of the Whitehead conjecture: the
Whitehead sequence is a contracting homotopy for the Goodwillie tower
of S^1 at the prime 2.
(2) Real homotopy theory of semi-algebraic sets
by Robert Hardt, Pascal Lambrechts, Victor Turchin and Ismar Volic
We complete the details of a theory outlined by Kontsevich and
Soibelman that associates to a semi-algebraic set a certain graded
commutative differential algebra of `semi-algebraic differential
forms' in a functorial way. This algebra encodes the real homotopy
type of the semi-algebraic set in the spirit of the de Rham algebra of
differential forms on a smooth manifold. Its development is needed
for Kontsevich's proof of the formality of the little cubes operad.
(3) The cactus tree of a metric space
by Panos Papasoglu and Eric Swenson
We extend the cactus theorem of Dinitz, Karzanov, Lomonosov to metric
spaces. In particular we show that if X is a separable continuum which
is not separated by n-1 points then the set of all n-tuples of points
separating X can be encoded by an R-tree.
(4) More on the anti-automorphism of the Steenrod algebra
by Vince Giambalvo and Haynes R Miller
The relations of Barratt and Miller are shown to include all relations
among the elements P^i * chi * P^{n-i} in the mod p Steenrod algebra,
and a minimal set of relations is given.
(5) Z-Structures on product groups
by Carrie J Tirel
A Z-structure on a group G, defined by M Bestvina, is a pair (hX,Z) of
spaces such that hX is a compact ER, Z is a Z-set in hX, G acts
properly and cocompactly on X = hX-Z and the collection of translates
of any compact set in X forms a null sequence in hX. It is natural to
ask whether a given group admits a Z-structure. In this paper, we
show that if two groups each admit a Z-structure, then so do their
free and direct products.
(6) Paires de structures de contact sur les varietes de dimension trois
by Vincent Colin and Sebastiao Firmo
On introduit une notion de paire positive de structures de contact sur
les varietes de dimension trois qui generalise celle de Eliashberg et
Thurston [Confoliations, Univ. Lecture Series 13, Amer. Math. Soc.
(1998)] et Mitsumatsu [Ann. Inst. Fourier (Grenoble) 45 (1995)
1407--1421; Foliations: geometry and dynamics (Warsaw, 2000) World
Sci. Publ., River Edge, NJ (2002) 75--125]. Une telle paire "normale"
donne naissance a un champ de plans continu et localement integrable
lambda. On montre que si lambda est uniquement integrable et si les
structures de contact sont tendues, alors le feuilletage integral de
lambda est sans composante de Reeb d'ame homologue a zero. De plus,
dans ce cas, la variete ambiante porte un feuilletage sans composante
de Reeb. On demontre egalement un theoreme de stabilite "a la Reeb"
pour les paires positives de structures tendues.
We introduce the notion of a positive pair of contact structures of a
three dimensional manifold which generalises that of Eliashberg,
Thurston and Mitsumatsu. A normal such pair gives rise to a
continuous, locally integrable plane field lambda. We show that if
lambda is uniquely integrable and if the contact structures are tight
then the integral foliation of lambda has no Reeb component whose core
is homologous to zero. Moreover, in this case, the ambient manifold
carries a foliation without a Reeb component. We also show a Reeb
stability theorem for positive pairs of tight structures.
(7) Topological classification of torus manifolds which have
codimension one extended actions
by Suyoung Choi and Shintaro Kuroki
A toric manifold is a compact non-singular toric variety. A torus
manifold is an oriented, closed, smooth manifold of dimension 2n with an
effective action of a compact torus T^n having a non-empty fixed point
set. Hence, a torus manifold can be thought of as a generalization of a
toric manifold. In the present paper, we focus on a certain class M in
the family of torus manifolds with codimension one extended actions,
and we give a topological classification of M. As a result, their
topological types are completely determined by their cohomology rings
and real characteristic classes.
The problem whether the cohomology ring determines the topological
type of a toric manifold or not is one of the most interesting open
problems in toric topology. One can also ask this problem for the
class of torus manifolds. Our results provide a negative answer to
this problem for torus manifolds. However, we find a sub-class of torus
manifolds with codimension one extended actions which is not in the class
of toric manifolds but which is classified by their cohomology rings.
(8) Sutured Floer homology, sutured TQFT and noncommutative QFT
by Daniel V Mathews
We define a "sutured topological quantum field theory", motivated by
the study of sutured Floer homology of product 3-manifolds, and
contact elements. We study a rich algebraic structure of suture
elements in sutured TQFT, showing that it corresponds to contact
elements in sutured Floer homology. We use this approach to make
computations of contact elements in sutured Floer homology over Z of
sutured manifolds (D^2 x S^1, F x S^1) where F is finite. This
generalises previous results of the author over Z_2 coefficients. Our
approach elaborates upon the quantum field theoretic aspects of
sutured Floer homology, building a noncommutative Fock space, together
with a bilinear form deriving from a certain combinatorial partial
order; we show that the sutured TQFT of discs is isomorphic to this
Fock space.
(9) Studying uniform thickness II: Transversely nonsimple iterated torus knots
by Douglas J LaFountain
We prove that an iterated torus knot type in (S^3, xi_std) fails the
uniform thickness property (UTP) if and only if it is formed from
repeated positive cablings, which is precisely when an iterated torus
knot supports the standard contact structure. This is the first
complete UTP classification for a large class of knots. We also show
that all iterated torus knots that fail the UTP support cabling knot
types that are transversely nonsimple.
(10) Quantum traces for representations of surface groups in SL_2(C)
by Francis Bonahon and Helen Wong
We relate two different quantizations of the character variety
consisting of all representations of surface groups in SL_2. One is
the Kauffman skein algebra considered by Bullock, Frohman and
Kania-Bartoszynska, Przytycki and Sikora, and Turaev. The other is the
quantum Teichmuller space introduced by Chekhov and Fock and by
Kashaev. We construct a homomorphism from the skein algebra to the
quantum Teichmuller space which, when restricted to the classical
case, corresponds to the equivalence between these two algebras
through trace functions.
Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers
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