Ten papers published by Geometry & Topology Publications

Discussion in 'Math Research' started by Geometry and Topology, Sep 26, 2011.

  1. 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
     
    Geometry and Topology, Sep 26, 2011
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