Ten papers published by Geometry & Topology Publications

Discussion in 'Math Research' started by Geometry and Topology, Oct 30, 2011.

  1. Two papers have been published by Algebraic & Geometric Topology

    (1) Algebraic & Geometric Topology 11 (2011) 2903-2936
    Knotted Legendrian surfaces with few Reeb chords
    by Georgios Dimitroglou Rizell
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p093.xhtml
    DOI: 10.2140/agt.2011.11.2903

    (2) Algebraic & Geometric Topology 11 (2011) 2937-2939
    Erratum to the article Twisted Alexander polynomials and
    surjectivity of a group homomorphism
    by Teruaki Kitano, Masaaki Suzuki and Masaaki Wada
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p0C2.xhtml
    DOI: 10.2140/agt.2011.11.2937

    Eight papers have been published by Geometry & Topology

    (3) Geometry & Topology 15 (2011) 1883-1925
    Coarse differentiation and quasi-isometries of a class of solvable Lie groups I
    by Irine Peng
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p046.xhtml
    DOI: 10.2140/gt.2011.15.1883

    (4) Geometry & Topology 15 (2011) 1927-1981
    Coarse differentiation and quasi-isometries of a class of solvable Lie groups II
    by Irine Peng
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p047.xhtml
    DOI: 10.2140/gt.2011.15.1927

    (5) Geometry & Topology 15 (2011) 1983-2015
    On the moduli space of positive Ricci curvature metrics on homotopy spheres
    by David J Wraith
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p048.xhtml
    DOI: 10.2140/gt.2011.15.1983

    (6) Geometry & Topology 15 (2011) 2017-2071
    Infinitesimal projective rigidity under Dehn filling
    by Michael Heusener and Joan Porti
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p049.xhtml
    DOI: 10.2140/gt.2011.15.2017

    (7) Geometry & Topology 15 (2011) 2073-2089
    Veering triangulations admit strict angle structures
    by Craig D Hodgson, J Hyam Rubinstein, Henry Segerman and Stephan Tillmann
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p050.xhtml
    DOI: 10.2140/gt.2011.15.2073

    (8) Geometry & Topology 15 (2011) 2091-2110
    Symplectic embeddings of ellipsoids in dimension greater than four
    by Olguta Buse and Richard Hind
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p051.xhtml
    DOI: 10.2140/gt.2011.15.2091

    (9) Geometry & Topology 15 (2011) 2111-2133
    Hodge theory on nearly Kahler manifolds
    by Misha Verbitsky
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p052.xhtml
    DOI: 10.2140/gt.2011.15.2111

    (10) Geometry & Topology 15 (2011) 2135-2180
    Asymptotics of the colored Jones function of a knot
    by Stavros Garoufalidis and Thang T Q Le
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p053.xhtml
    DOI: 10.2140/gt.2011.15.2135

    Abstracts follow

    (1) Knotted Legendrian surfaces with few Reeb chords
    by Georgios Dimitroglou Rizell

    For g>0, we construct g+1 Legendrian embeddings of a surface of genus
    g into J^1(R^2)=R^5 which lie in pairwise distinct Legendrian isotopy
    classes and which all have g+1 transverse Reeb chords (g+1 is the
    conjecturally minimal number of chords). Furthermore, for g of the g+1
    embeddings the Legendrian contact homology DGA does not admit any
    augmentation over Z_2, and hence cannot be linearized. We also
    investigate these surfaces from the point of view of the theory of
    generating families. Finally, we consider Legendrian spheres and
    planes in J^1(S^2) from a similar perspective.


    (2) Erratum to the article Twisted Alexander polynomials and
    surjectivity of a group homomorphism
    by Teruaki Kitano, Masaaki Suzuki and Masaaki Wada

    We prove the nonexistence of surjective homomorphisms from knot groups
    G(8_{21}), G(9_{12}), G(9_{24}), G(9_{39}) onto G(4_1) using twisted
    Alexander polynomials and the numbers of surjective homomorphisms onto
    SL(2;Z/7Z).


    (3) Coarse differentiation and quasi-isometries of a class of solvable Lie groups I
    by Irine Peng

    This is the first of two consecutive papers that aim to understand
    quasi-isometries of a class of unimodular split solvable Lie groups.
    In the present paper, we show that locally (in a coarse sense), a
    quasi-isometry between two groups in this class is close to a map that
    respects their group structures. In the following paper we will use
    this result to show quasi-isometric rigidity.


    (4) Coarse differentiation and quasi-isometries of a class of solvable Lie groups II
    by Irine Peng

    In this paper, we continue with the results of the preceeding paper
    and compute the group of quasi-isometries for a subclass of split
    solvable unimodular Lie groups. Consequently, we show that any
    finitely generated group quasi-isometric to a member of the subclass
    has to be polycyclic and is virtually a lattice in an
    abelian-by-abelian solvable Lie group. We also give an example of a
    unimodular solvable Lie group that is not quasi-isometric to any
    finitely generated group, as well deduce some quasi-isometric rigidity
    results.


    (5) On the moduli space of positive Ricci curvature metrics on homotopy spheres
    by David J Wraith

    We show that the moduli space of Ricci positive metrics on a certain
    family of homotopy spheres has infinitely many components.


    (6) Infinitesimal projective rigidity under Dehn filling
    by Michael Heusener and Joan Porti

    To a hyperbolic manifold one can associate a canonical projective
    structure and a fundamental question is whether or not it can be
    deformed. In particular, the canonical projective structure of a
    finite volume hyperbolic manifold with cusps might have deformations
    which are trivial on the cusps.

    The aim of this article is to prove that if the canonical projective
    structure on a cusped hyperbolic manifold M is infinitesimally
    projectively rigid relative to the cusps, then infinitely many
    hyperbolic Dehn fillings on M are locally projectively rigid. We
    analyze in more detail the figure eight knot and the Whitehead link
    exteriors, for which we can give explicit infinite families of slopes
    with projectively rigid Dehn fillings.


    (7) Veering triangulations admit strict angle structures
    by Craig D Hodgson, J Hyam Rubinstein, Henry Segerman and Stephan Tillmann

    Agol recently introduced the concept of a veering taut triangulation
    of a 3-manifold, which is a taut ideal triangulation with some extra
    combinatorial structure. We define the weaker notion of a "veering
    triangulation" and use it to show that all veering triangulations
    admit strict angle structures. We also answer a question of Agol,
    giving an example of a veering taut triangulation that is not layered.


    (8) Symplectic embeddings of ellipsoids in dimension greater than four
    by Olguta Buse and Richard Hind

    We study symplectic embeddings of ellipsoids into balls. In the main
    construction, we show that a given embedding of 2m-dimensional
    ellipsoids can be suspended to embeddings of ellipsoids in any higher
    dimension. In dimension 6,s if the ratio of the areas of any two axes
    is sufficiently large then the ellipsoid is flexible in the sense that
    it fully fills a ball. We also show that the same property holds in
    all dimensions for sufficiently thin ellipsoids E(1,..., a). A
    consequence of our study is that in arbitrary dimension a ball can be
    fully filled by any sufficiently large number of identical smaller
    balls, thus generalizing a result of Biran valid in dimension 4.


    (9) Hodge theory on nearly Kahler manifolds
    by Misha Verbitsky

    Let (M,I,omega,Omega) be a nearly Kahler 6-manifold, that is, an
    SU(3)-manifold with (3,0)-form Omega and Hermitian form omega which
    satisfies domega=3*lambda*Re(Omega), d Im(Omega)=-2*lambda*omega^2,
    for a nonzero real constant lambda. We develop an analogue of the
    Kahler relations on M, proving several useful identities for various
    intrinsic Laplacians on M. When M is compact, these identities give
    powerful results about cohomology of M. We show that harmonic forms
    on M admit a Hodge decomposition, and prove that H^{p,q}(M)=0 unless
    p=q or (p=1,q=2) or (p=2,q=1).


    (10) Asymptotics of the colored Jones function of a knot
    by Stavros Garoufalidis and Thang T Q Le

    To a knot in 3-space, one can associate a sequence of Laurent
    polynomials, whose n-th term is the n-th colored Jones polynomial. The
    paper is concerned with the asymptotic behavior of the value of the
    n-th colored Jones polynomial at e^{a/n}, when a is a fixed complex
    number and n tends to infinity. We analyze this asymptotic behavior
    to all orders in 1/n when a is a sufficiently small complex number.
    In addition, we give upper bounds for the coefficients and degree of
    the n-th colored Jones polynomial, with applications to upper bounds
    in the Generalized Volume Conjecture. Work of Agol, Dunfield, Storm
    and W Thurston implies that our bounds are asymptotically
    optimal. Moreover, we give results for the Generalized Volume
    Conjecture when a is near 2*pi*i. Our proofs use crucially the
    cyclotomic expansion of the colored Jones function, due to Habiro.



    Geometry & Topology Publications is an imprint of
    Mathematical Sciences Publishers
     
    Geometry and Topology, Oct 30, 2011
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