Nine papers published by Geometry & Topology Publications

Discussion in 'Math Research' started by Geometry and Topology, Oct 15, 2011.

  1. Four papers have been published by Algebraic & Geometric Topology:

    (1) Algebraic & Geometric Topology 11 (2011) 2775-2814
       Delta-discrete G-spectra and iterated homotopy fixed points
         by Daniel G Davis
       URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p089.xhtml
       DOI: 10.2140/agt.2011.11.2775

    (2) Algebraic & Geometric Topology 11 (2011) 2815-2827
       A loop theorem/Dehn's lemma for some orbifolds
         by Josh Barnard
       URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p090.xhtml
       DOI: 10.2140/agt.2011.11.2815

    (3) Algebraic & Geometric Topology 11 (2011) 2829-2860
       Spectral sequences in string topology
         by Lennart Meier
       URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p091.xhtml
       DOI: 10.2140/agt.2011.11.2829

    (4) Algebraic & Geometric Topology 11 (2011) 2861-2901
       On the derivation algebra of the free Lie algebra and trace maps
         by Naoya Enomoto and Takao Satoh
       URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p092.xhtml
       DOI: 10.2140/agt.2011.11.2861

    Five papers have been published by Geometry & Topology;
    papers (5)--(8) complete Volume 15 Issue 3, paper (9) opens
    Issue 4:

    (5) Geometry & Topology 15 (2011) 1617-1650
       Homological Lagrangian monodromy
         by Shengda Hu, Franois Lalonde and Remi Leclercq
       URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p041.xhtml
       DOI: 10.2140/gt.2011.15.1617

    (6) Geometry & Topology 15 (2011) 1651-1706
       The moduli space of stable quotients
         by Alina Marian, Dragos Oprea and Rahul Pandharipande
       URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p042.xhtml
       DOI: 10.2140/gt.2011.15.1651

    (7) Geometry & Topology 15 (2011) 1707-1747
       Parallelogram decompositions and generic surfaces in H^hyp(4)
         by Duc-Manh Nguyen
       URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p043.xhtml
       DOI: 10.2140/gt.2011.15.1707

    (8) Geometry & Topology 15 (2011) 1749-1842
       Sutures and contact homology I
         by Vincent Colin, Paolo Ghiggini, Ko Honda and Michael Hutchings
       URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p044.xhtml
       DOI: 10.2140/gt.2011.15.1749

    (9) Geometry & Topology 15 (2011) 1843-1882
       On exceptional quotient singularities
         by Ivan Cheltsov and Constantin Shramov
       URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p045.xhtml
       DOI: 10.2140/gt.2011.15.1843

    Abstracts follow

    (1) Delta-discrete G-spectra and iterated homotopy fixed points
         by Daniel G Davis

    Let G be a profinite group with finite virtual cohomological dimension
    and let X be a discrete G-spectrum. If H and K are closed subgroups of
    G, with H normal in K, then, in general, the K/H-spectrum X^{hH} is
    not known to be a continuous K/H-spectrum, so that it is not known (in
    general) how to define the iterated homotopy fixed point spectrum
    (X^{hH})^{hK/H}. To address this situation, we define homotopy fixed
    points for delta-discrete G-spectra and show that the setting of
    delta-discrete G-spectra gives a good framework within which to work.
    In particular, we show that by using delta-discrete K/H-spectra, there
    is always an iterated homotopy fixed point spectrum, denoted
    (X^{hH})^{h_delta K/H}, and it is just X^{hK}.

    Additionally, we show that for any delta-discrete G-spectrum Y, there
    is an equivalence (Y^{h_delta H})^{h_delta K/H} ~= Y^{h_delta K}.
    Furthermore, if G is an arbitrary profinite group, there is a
    delta-discrete G-spectrum X_delta that is equivalent to X and, though
    X^{hH} is not even known in general to have a K/H-action, there is
    always an equivalence ((X_\delta)^{h_delta H})^{h_delta K/H} ~=
    (X_delta)^{h_delta K}. Therefore, delta-discrete L-spectra, by letting
    L equal H, K and K/H, give a way of resolving undesired deficiencies
    in our understanding of homotopy fixed points for discrete G-spectra.


    (2) A loop theorem/Dehn's lemma for some orbifolds
         by Josh Barnard

    The equivariant loop theorem implies the existence of a loop
    theorem/Dehn's lemma for 3-orbifolds that are good (covered by a
    3-manifold). In this note we prove a loop theorem/Dehn's lemma for any
    locally orientable 3-orbifold (good or bad) whose singular set is
    labeled with powers of 2. The proof is modeled on the standard tower
    construction.


    (3) Spectral sequences in string topology
         by Lennart Meier

    In this paper, we investigate the behavior of the Serre spectral
    sequence with respect to the algebraic structures of string topology
    in generalized homology theories, specifically with the Chas-Sullivan
    product and the corresponding coproduct and module structures.  We
    prove compatibility for two kinds of fiber bundles: the fiber bundle
    Omega^n M -> L^n M -> M for an h_*-oriented manifold M and the looped
    fiber bundle L^n F -> L^n E -> L^n B of a fiber bundle F -> E -> B of
    h_*-oriented manifolds.  Our method lies in the construction of Gysin
    morphisms of spectral sequences.  We apply these results to study the
    ordinary homology of the free loop spaces of sphere bundles and some
    generalized homologies of the free loop spaces of spheres and
    projective spaces.  For the latter purpose, we construct explicit
    manifold generators for the homology of these spaces.


    (4) On the derivation algebra of the free Lie algebra and trace maps
         by Naoya Enomoto and Takao Satoh

    We mainly study the derivation algebra of the free Lie algebra and the
    Chen Lie algebra generated by the abelianization H of a free group,
    and trace maps.  To begin with, we give the irreducible decomposition
    of the derivation algebra as a GL(n,Q)-module via the Schur-Weyl
    duality and some tensor product theorems for GL(n,Q).  Using them, we
    calculate the irreducible decomposition of the images of the Johnson
    homomorphisms of the automorphism group of a free group and a free
    metabelian group.

    Next, we consider some applications of trace maps: Morita's trace map
    and the trace map for the exterior product of H.  First, we determine
    the abelianization of the derivation algebra of the Chen Lie algebra
    as a Lie algebra, and show that the abelianization is given by the
    degree one part and Morita's trace maps.  Second, we consider twisted
    cohomology groups of the automorphism group of a free nilpotent group.
    In particular, we show that the trace map for the exterior product of
    H defines a nontrivial twisted second cohomology class of it.


    (5) Homological Lagrangian monodromy
         by Shengda Hu, Francois Lalonde and Remi Leclercq

    We show that the Hamiltonian Lagrangian monodromy group, in its
    homological version, is trivial for any weakly exact Lagrangian
    submanifold of a symplectic manifold. The proof relies on a sheaf
    approach to Floer homology given by a relative Seidel morphism.


    (6) The moduli space of stable quotients
         by Alina Marian, Dragos Oprea and Rahul Pandharipande

    A moduli space of stable quotients of the rank n trivial sheaf on
    stable curves is introduced.  Over nonsingular curves, the moduli
    space is Grothendieck's Quot scheme. Over nodal curves, a relative
    construction is made to keep the torsion of the quotient away from the
    singularities.  New compactifications of classical spaces arise
    naturally: a nonsingular and irreducible compactification of the
    moduli of maps from genus 1 curves to projective space is obtained.
    Localization on the moduli of stable quotients leads to new relations
    in the tautological ring generalizing Brill-Noether constructions.

    The moduli space of stable quotients is proven to carry a canonical
    2-term obstruction theory and thus a virtual class.  The resulting
    system of descendent invariants is proven to equal the Gromov-Witten
    theory of the Grassmannian in all genera. Stable quotients can also be
    used to study Calabi-Yau geometries.  The conifold is calculated to
    agree with stable maps. Several questions about the behavior of stable
    quotients for arbitrary targets are raised.


    (7) Parallelogram decompositions and generic surfaces in H^hyp(4)
         by Duc-Manh Nguyen

    The space H^hyp(4) is the moduli space of pairs (M,omega), where M is
    a hyperelliptic Riemann surface of genus 3 and omega is a holomorphic
    1-form having only one zero. In this paper, we first show that every
    surface in H^hyp(4) admits a decomposition into parallelograms and
    simple cylinders following a unique model. We then show that if this
    decomposition satisfies some irrational condition, then the
    GL^+(2,R)-orbit of the surface is dense in H^hyp(4); such surfaces are
    called generic. Using this criterion, we prove that there are generic
    surfaces in H^hyp(4) with coordinates in any quadratic field, and
    there are Thurston-Veech surfaces with trace field of degree three
    over Q which are generic.


    (8) Sutures and contact homology I
         by Vincent Colin, Paolo Ghiggini, Ko Honda and Michael Hutchings

    We define a relative version of contact homology for contact manifolds
    with convex boundary and prove basic properties of this relative
    contact homology.  Similar considerations also hold for embedded
    contact homology.


    (9) On exceptional quotient singularities
         by Ivan Cheltsov and Constantin Shramov

    We study exceptional quotient singularities. In particular, we prove
    an exceptionality criterion in terms of the alpha-invariant of Tian,
    and utilize it to classify four-dimensional and five-dimensional
    exceptional quotient singularities.



      Geometry & Topology Publications is an imprint of
      Mathematical Sciences Publishers.
     
    Geometry and Topology, Oct 15, 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.