Nine papers published by Geometry & Topology Publications

Discussion in 'Math Research' started by Geometry and Topology, Aug 10, 2011.

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

    (1) Algebraic & Geometric Topology 11 (2011) 2167-2190
       An algorithm for finding parameters of tunnels
         by Kai Ishihara
       URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p070.xhtml
       DOI: 10.2140/agt.2011.11.2167

    (2) Algebraic & Geometric Topology 11 (2011) 2191-2205
       Quantum invariants of random 3-manifolds
         by Nathan M Dunfield and Helen Wong
       URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p071.xhtml
       DOI: 10.2140/agt.2011.11.2191

    (3) Algebraic & Geometric Topology 11 (2011) 2207-2235
       Flat structures on surface bundles
         by Jonathan Bowden
       URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p072.xhtml
       DOI: 10.2140/agt.2011.11.2207

    Six papers have been published by Geometry & Topology

    (4) Geometry & Topology 15 (2011) 1225-1295
       Connected components of the compactification of representation
    spaces of surface groups
         by Maxime Wolff
       URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p033.xhtml
       DOI: 10.2140/gt.2011.15.1225

    (5) Geometry & Topology 15 (2011) 1297-1312
       Minimal pseudo-Anosov translation lengths on the complex of curves
         by Vaibhav Gadre and Chia-Yen Tsai
       URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p034.xhtml
       DOI: 10.2140/gt.2011.15.1297

    (6) Geometry & Topology 15 (2011) 1313-1417
       Deformed Hamiltonian Floer theory, capacity estimates and Calabi
    quasimorphisms
         by Michael Usher
       URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p035.xhtml
       DOI: 10.2140/gt.2011.15.1313

    (7) Geometry & Topology 15 (2011) 1419-1475
       Line patterns in free groups
         by Christopher H Cashen and Natasa Macura
       URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p036.xhtml
       DOI: 10.2140/gt.2011.15.1419

    (8) Geometry & Topology 15 (2011) 1477-1508
       Isosystolic genus three surfaces critical for slow metric variations
         by Stephane Sabourau
       URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p037.xhtml
       DOI: 10.2140/gt.2011.15.1477

    (9) Geometry & Topology 15 (2011) 1509-1543
       Non-commutative Donaldson-Thomas theory and vertex operators
         by Kentaro Nagao
       URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p038.xhtml
       DOI: 10.2140/gt.2011.15.1509

    Abstracts follow

    (1) An algorithm for finding parameters of tunnels
         by Kai Ishihara

    Cho and McCullough gave a numerical parameterization of the collection
    of all
    tunnels of all tunnel number 1 knots and links in the 3-sphere.  Here we
    give an algorithm for finding the parameter of a given tunnel by using
    its
    Heegaard diagram.


    (2) Quantum invariants of random 3-manifolds
         by Nathan M Dunfield and Helen Wong

    We consider the SO(3) Witten-Reshetikhin-Turaev quantum invariants of
    random 3-manifolds.  When the level r is prime, we show that the
    asymptotic distribution of the absolute value of these invariants is
    given by a Rayleigh distribution which is independent of the choice of
    level.  Hence the probability that the quantum invariant certifies the
    Heegaard genus of a random 3-manifold of a fixed Heegaard genus g is
    positive but very small, less than 10^-7 except when g<=3.  We also
    examine random surface bundles over the circle and find the same
    distribution for quantum invariants there.


    (3) Flat structures on surface bundles
         by Jonathan Bowden

    We show that there exist flat surface bundles with closed leaves having
    nontrivial normal bundles. This leads us to compute the abelianisation
    of
    surface diffeomorphism groups with marked points. We also extend a
    formula of
    Tsuboi that expresses the Euler class of a flat circle bundle in terms
    of the
    Calabi invariant of certain Hamiltonian diffeomorphisms to surfaces of
    higher
    genus and derive a similar formula for the first MMM-class of surface
    bundles
    with punctured fibre.


    (4) Connected components of the compactification of representation
    spaces of surface groups
         by Maxime Wolff

    The Thurston compactification of Teichmuller spaces has been
    generalised to many different representation spaces by Morgan, Shalen,
    Bestvina, Paulin, Parreau and others. In the simplest case of
    representations of fundamental groups of closed hyperbolic surfaces in
    PSL(2,R), we prove that this compactification behaves very badly: the
    nice behaviour of the Thurston compactification of the Teichmuller
    space contrasts with wild phenomena happening on the boundary of the
    other connected components of these representation spaces. We prove
    that it is more natural to consider a refinement of this
    compactification, which remembers the orientation of the hyperbolic
    plane. The ideal points of this compactification are oriented R-trees,
    ie, R-trees equipped with a planar structure.


    (5) Minimal pseudo-Anosov translation lengths on the complex of curves
         by Vaibhav Gadre and Chia-Yen Tsai

    We establish bounds on the minimal asymptotic pseudo-Anosov
    translation lengths on the complex of curves of orientable
    surfaces. In particular, for a closed surface with genus g at least 2,
    we show that there are positive constants a_1 < a_2 such that the
    minimal translation length is bounded below and above by a_1/g^2 and
    a_2/g^2.


    (6) Deformed Hamiltonian Floer theory, capacity estimates and Calabi
    quasimorphisms
         by Michael Usher

    We develop a family of deformations of the differential and of the
    pair-of-pants product on the Hamiltonian Floer complex of a symplectic
    manifold (M,omega) which upon passing to homology yields ring
    isomorphisms with the *big* quantum homology of M.  By studying the
    properties of the resulting deformed version of the Oh-Schwarz
    spectral invariants, we obtain a Floer-theoretic interpretation of a
    result of Lu which bounds the Hofer-Zehnder capacity of M when M has a
    nonzero Gromov-Witten invariant with two point constraints, and we
    produce a new algebraic criterion for (M,omega) to admit a Calabi
    quasimorphism and a symplectic quasistate.  This latter criterion is
    found to hold whenever M has generically semisimple quantum homology
    in the sense considered by Dubrovin and Manin (this includes all
    compact toric M), and also whenever M is a point blowup of an
    arbitrary closed symplectic manifold.


    (7) Line patterns in free groups
         by Christopher H Cashen and Natasa Macura

    We study line patterns in a free group by considering the topology of
    the decomposition space, a quotient of the boundary at infinity of the
    free group related to the line pattern.  We show that the group of
    quasi-isometries preserving a line pattern in a free group acts by
    isometries on a related space if and only if there are no cut pairs in
    the decomposition space.  We also give an algorithm to detect such cut
    pairs.


    (8) Isosystolic genus three surfaces critical for slow metric variations
         by Stephane Sabourau

    We show that the two piecewise flat surfaces with conical
    singularities conjectured by E Calabi as extremal surfaces for the
    isosystolic problem in genus 3 are critical with respect to some
    metric variations.  The proof relies on a new approach to study
    isosystolic extremal surfaces.


    (9) Non-commutative Donaldson-Thomas theory and vertex operators
         by Kentaro Nagao

    In [K Nagao, Refined open non-commutative Donaldson--Thomas theory
    for small toric Calabi-Yau 3-folds, Pacific J. Math. (to appear),
    arXiv:0907.3784], we introduced a variant of non-commutative
    Donaldson-Thomas theory in a combinatorial way, which is related to the
    topological vertex by a wall-crossing phenomenon.  In this paper, we (1)
    provide an alternative definition in a geometric way, (2) show that the
    two definitions agree with each other and (3) compute the invariants
    using the vertex operator method, following [A Okounkov, N Reshetikhin,
    C Vafa, Quantum Calabi-Yau and classical crystals, from: "The unity
    of mathematics", Progr. Math., Birkhauser (2006) 597--618] and [B Young,
    Generating functions for colored 3D Young diagrams and the
    Donaldson-Thomas invariants of orbifolds, Duke Math. J. 152 (2010)
    115--153].  The stability parameter in the geometric definition
    determines the order of the vertex operators and hence we can understand
    the wall-crossing formula in non-commutative Donaldson-Thomas theory as
    the commutator relation of the vertex operators.



      Geometry & Topology Publications is an imprint of
      Mathematical Sciences Publishers
     
    Geometry and Topology, Aug 10, 2011
    #1
    1. Advertisements

Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.