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Ten papers published by Geometry & Topology Publications
Posted:
Sep 26, 2011 10:30 AM


Nine papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 24532475 The Goodwillie tower for S^1 and Kuhn's Theorem by Mark Behrens URL: http://www.msp.warwick.ac.uk/agt/2011/1104/p080.xhtml DOI: 10.2140/agt.2011.11.2453
(2) Algebraic & Geometric Topology 11 (2011) 24772545 Real homotopy theory of semialgebraic sets by Robert Hardt, Pascal Lambrechts, Victor Turchin and Ismar Volic URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p081.xhtml DOI: 10.2140/agt.2011.11.2477
(3) Algebraic & Geometric Topology 11 (2011) 25472578 The cactus tree of a metric space by Panos Papasoglu and Eric Swenson URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p082.xhtml DOI: 10.2140/agt.2011.11.2547
(4) Algebraic & Geometric Topology 11 (2011) 25792585 More on the antiautomorphism of the Steenrod algebra by Vince Giambalvo and Haynes R Miller URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p083.xhtml DOI: 10.2140/agt.2011.11.2579
(5) Algebraic & Geometric Topology 11 (2011) 25872625 ZStructures on product groups by Carrie J Tirel URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p084.xhtml DOI: 10.2140/agt.2011.11.2587
(6) Algebraic & Geometric Topology 11 (2011) 26272653 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/2011/1105/p085.xhtml DOI: 10.2140/agt.2011.11.2627
(7) Algebraic & Geometric Topology 11 (2011) 26552679 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/2011/1105/p086.xhtml DOI: 10.2140/agt.2011.11.2655
(8) Algebraic & Geometric Topology 11 (2011) 26812739 Sutured Floer homology, sutured TQFT and noncommutative QFT by Daniel V Mathews URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p087.xhtml DOI: 10.2140/agt.2011.11.2681
(9) Algebraic & Geometric Topology 11 (2011) 27412774 Studying uniform thickness II: Transversely nonsimple iterated torus knots by Douglas J LaFountain URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p088.xhtml DOI: 10.2140/agt.2011.11.2741
One paper has been published by Geometry & Topology
(10) Geometry & Topology 15 (2011) 15691615 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/2011/1503/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 2local Goodwillie tower of the identity evaluated at S^1. We show that they exhibit the same homological behavior as the JamesHopf maps used by N Kuhn to prove the 2primary 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 semialgebraic 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 semialgebraic set a certain graded commutative differential algebra of `semialgebraic differential forms' in a functorial way. This algebra encodes the real homotopy type of the semialgebraic 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 n1 points then the set of all ntuples of points separating X can be encoded by an Rtree.
(4) More on the antiautomorphism 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^{ni} in the mod p Steenrod algebra, and a minimal set of relations is given.
(5) ZStructures on product groups by Carrie J Tirel
A Zstructure 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 Zset in hX, G acts properly and cocompactly on X = hXZ 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 Zstructure. In this paper, we show that if two groups each admit a Zstructure, 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) 14071421; Foliations: geometry and dynamics (Warsaw, 2000) World Sci. Publ., River Edge, NJ (2002) 75125]. 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 nonsingular 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 nonempty 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 subclass 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 3manifolds, 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 KaniaBartoszynska, 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



