Eleven papers published by GTP completing 2011 publication

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

  1. This announcement completes GTP publication for 2011.

    Papers (1)-(5) complete AGT Volume 11 (2011) and papers (6)-(11)
    complete GT Volume 15 (2011). Publiction in 2012 will commence on
    January 1 2012. Seasons greetings to all!

    Five papers have been published by Algebraic & Geometric Topology

    (1) Algebraic & Geometric Topology 11 (2011) 2941-2970
    Representation spaces of pretzel knots
    by Raphael Zentner
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p095.xhtml
    DOI: 10.2140/agt.2011.11.2941

    (2) Algebraic & Geometric Topology 11 (2011) 2971-3010
    Reducible braids and Garside Theory
    by Juan Gonzalez-Meneses and Bert Wiest
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p096.xhtml
    DOI: 10.2140/agt.2011.11.2971

    (3) Algebraic & Geometric Topology 11 (2011) 3011-3041
    Representation stability for the cohomology of the moduli space M_g^n
    by Rita Jimenez Rolland
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p097.xhtml
    DOI: 10.2140/agt.2011.11.3011

    (4) Algebraic & Geometric Topology 11 (2011) 3043-3064
    The Fox property for codimension one embeddings of products of three spheres into spheres
    by Laercio Aparecido Lucas and Osamu Saeki
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p098.xhtml
    DOI: 10.2140/agt.2011.11.3043

    (5) Algebraic & Geometric Topology 11 (2011) 3065-3084
    Constructing free actions of p-groups on products of spheres
    by Michele Klaus
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p099.xhtml
    DOI: 10.2140/agt.2011.11.3065

    Six papers have been published by Geometry & Topology

    (6) Geometry & Topology 15 (2011) 2181-2233
    Strongly contracting geodesics in Outer Space
    by Yael Algom-Kfir
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p054.xhtml
    DOI: 10.2140/gt.2011.15.2181

    (7) Geometry & Topology 15 (2011) 2235-2273
    Rigidity of spherical codes
    by Henry Cohn, Yang Jiao, Abhinav Kumar and Salvatore Torquato
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p055.xhtml
    DOI: 10.2140/gt.2011.15.2235

    (8) Geometry & Topology 15 (2011) 2275-2298
    On intrinsic geometry of surfaces in normed spaces
    by Dmitri Burago and Sergei Ivanov
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p056.xhtml
    DOI: 10.2140/gt.2011.15.2275

    (9) Geometry & Topology 15 (2011) 2299-2319
    Rigidity of polyhedral surfaces, III
    by Feng Luo
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p057.xhtml
    DOI: 10.2140/gt.2011.15.2299

    (10) Geometry & Topology 15 (2011) 2321-2350
    Counting lattice points in compactified moduli spaces of curves
    by Norman Do and Paul Norbury
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p058.xhtml
    DOI: 10.2140/gt.2011.15.2321

    (11) Geometry & Topology 15 (2011) 2351-2457
    Intersection theory of punctured pseudoholomorphic curves
    by Richard Siefring
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p059.xhtml
    DOI: 10.2140/gt.2011.15.2351

    Abstracts follow

    (1) Representation spaces of pretzel knots
    by Raphael Zentner

    We study the representation spaces R(K;i) appearing in Kronheimer and
    Mrowka's instanton knot Floer homologies for a class of pretzel
    knots. In particular, for pretzel knots P(p,q,r) with p, q, r pairwise
    coprime, these appear to be nondegenerate and comprise representations
    in SU(2) that are not binary dihedral.


    (2) Reducible braids and Garside Theory
    by Juan Gonzalez-Meneses and Bert Wiest

    We show that reducible braids which are, in a Garside-theoretical
    sense, as simple as possible within their conjugacy class, are also as
    simple as possible in a geometric sense. More precisely, if a braid
    belongs to a certain subset of its conjugacy class which we call the
    stabilized set of sliding circuits, and if it is reducible, then its
    reducibility is geometrically obvious: it has a round or almost round
    reducing curve. Moreover, for any given braid, an element of its
    stabilized set of sliding circuits can be found using the well-known
    cyclic sliding operation. This leads to a polynomial time algorithm
    for deciding the Nielsen-Thurston type of any braid, modulo one
    well-known conjecture on the speed of convergence of the cyclic
    sliding operation.


    (3) Representation stability for the cohomology of the moduli space M_g^n
    by Rita Jimenez Rolland

    Let M_g^n be the moduli space of Riemann surfaces of genus g with n
    labeled marked points. We prove that, for g >= 2, the cohomology
    groups {H^i(M_g^n;Q)}_{n=1}^{\infty} form a sequence of
    S_n-representations which is representation stable in the sense of
    Church-Farb. In particular this result applied to the trivial
    S_n-representation implies rational "puncture homological stability"
    for the mapping class group Mod_g^n. We obtain representation
    stability for sequences {H^i(PMod^n(M);Q)}_{n=1}^{\infty}, where
    PMod^n(M) is the mapping class group of many connected orientable
    manifolds M of dimension d >= 3 with centerless fundamental group; and
    for sequences {H^i(BPDiff^n(M);Q)}_{n=1}^{\infty}, where BPDiff^n(M)
    is the classifying space of the subgroup PDiff^n(M) of diffeomorphisms
    of M that fix pointwise n distinguished points in M.


    (4) The Fox property for codimension one embeddings of products of three spheres into spheres
    by Laercio Aparecido Lucas and Osamu Saeki

    Fox has shown that for every closed connected surface smoothly
    embedded in S^3, the closure of each component of its complement is
    diffeomorphic to the closure of the complement of a handlebody
    embedded in S^3. In this paper, we study a similar `Fox property'
    for smooth embeddings of S^p x S^q x S^r in S^{p+q+r+1}.


    (5) Constructing free actions of p-groups on products of spheres
    by Michele Klaus

    We prove that, for p an odd prime, every finite p-group of rank 3 acts
    freely on a finite complex X homotopy equivalent to a product of three
    spheres.


    (6) Strongly contracting geodesics in Outer Space
    by Yael Algom-Kfir

    We study the Lipschitz metric on Outer Space and prove that fully
    irreducible elements of Out(F_n) act by hyperbolic isometries with axes
    which are strongly contracting. As a corollary, we prove that the axes of
    fully irreducible automorphisms in the Cayley graph of Out(F_n) are Morse,
    meaning that a quasi-geodesic with endpoints on the axis stays within
    a bounded distance from the axis.


    (7) Rigidity of spherical codes
    by Henry Cohn, Yang Jiao, Abhinav Kumar and Salvatore Torquato

    A packing of spherical caps on the surface of a sphere (that is, a
    spherical code) is called rigid or jammed if it is isolated within the
    space of packings. In other words, aside from applying a global isometry,
    the packing cannot be deformed. In this paper, we systematically study
    the rigidity of spherical codes, particularly kissing configurations.
    One surprise is that the kissing configuration of the Coxeter-Todd
    lattice is not jammed, despite being locally jammed (each individual
    cap is held in place if its neighbors are fixed); in this respect, the
    Coxeter-Todd lattice is analogous to the face-centered cubic lattice in
    three dimensions. By contrast, we find that many other packings have
    jammed kissing configurations, including the Barnes-Wall lattice and
    all of the best kissing configurations known in four through twelve
    dimensions. Jamming seems to become much less common for large kissing
    configurations in higher dimensions, and in particular it fails for
    the best kissing configurations known in 25 through 31 dimensions.
    Motivated by this phenomenon, we find new kissing configurations in
    these dimensions, which improve on the records set in 1982 by the
    laminated lattices.


    (8) On intrinsic geometry of surfaces in normed spaces
    by Dmitri Burago and Sergei Ivanov

    We prove three facts about intrinsic geometry of surfaces in a normed
    (Minkowski) space. When put together, these facts demonstrate a rather
    intriguing picture. We show that (1) geodesics on saddle surfaces (in
    a space of any dimension) behave as they are expected to: they have no
    conjugate points and thus minimize length in their homotopy class; (2)
    in contrast, every two-dimensional Finsler manifold can be locally
    embedded as a saddle surface in a 4-dimensional space; and (3)
    geodesics on convex surfaces in a 3-dimensional space also behave as
    they are expected to: on a complete strictly convex surface, no
    complete geodesic minimizes the length globally.


    (9) Rigidity of polyhedral surfaces, III
    by Feng Luo

    This paper investigates several global rigidity issues for polyhedral
    surfaces including inversive distance circle packings. Inversive
    distance circle packings are polyhedral surfaces introduced by P
    Bowers and K Stephenson in [Mem. Amer. Math. Soc. 170, no. 805,
    Amer. Math. Soc. (2004)] as a generalization of Andreev and
    Thurston's circle packing. They conjectured that inversive distance
    circle packings are rigid. We prove this conjecture using recent work
    of R Guo [Trans. Amer. Math. Soc. 363 (2011) 4757--4776] on the
    variational principle associated to the inversive distance circle
    packing. We also show that each polyhedral metric on a triangulated
    surface is determined by various discrete curvatures that we
    introduced in [arXiv 0612.5714], verifying a conjecture in [arXiv
    0612.5714]. As a consequence, we show that the discrete Laplacian
    operator determines a spherical polyhedral metric.


    (10) Counting lattice points in compactified moduli spaces of curves
    by Norman Do and Paul Norbury

    We define and count lattice points in the moduli space bar{M}_{g,n}
    of stable genus g curves with n labeled points. This extends a
    construction of the second author for the uncompactified moduli space
    M_{g,n}. The enumeration produces polynomials whose top degree
    coefficients are tautological intersection numbers on bar{M}_{g,n}
    and whose constant term is the orbifold Euler characteristic of
    bar{M}_{g,n}. We prove a recursive formula which can be used to
    effectively calculate these polynomials. One consequence of these
    results is a simple recursion relation for the orbifold Euler
    characteristic of bar{M}_{g,n}.


    (11) Intersection theory of punctured pseudoholomorphic curves
    by Richard Siefring
    We study the intersection theory of punctured pseudoholomorphic curves
    in 4-dimensional symplectic cobordisms. Using the asymptotic results
    of the author [Comm. Pure Appl. Math. 61(2008) 1631--84], we first
    study the local intersection properties of such curves at the
    punctures. We then use this to develop topological controls on the
    intersection number of two curves. We also prove an adjunction
    formula which gives a topological condition that will guarantee a
    curve in a given homotopy class is embedded, extending previous work
    of Hutchings [JEMS 4(2002) 313--61].

    We then turn our attention to curves in the symplectization R x M of a
    3-manifold M admitting a stable Hamiltonian structure. We investigate
    controls on intersections of the projections of curves to the
    3-manifold and we present conditions that will guarantee the
    projection of a curve to the 3-manifold is an embedding.

    Finally we consider an application concerning pseudoholomorphic curves
    in manifolds admitting a certain class of holomorphic open book
    decomposition and an application concerning the existence of
    generalized pseudoholomorphic curves, as introduced by Hofer
    [Geom. Func. Anal. (2000) 674--704] .



    Geometry & Topology Publications is an imprint of
    Mathematical Sciences Publishers
     
    Geometry and Topology, Dec 26, 2011
    #1
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