Eight papers published by Geometry & Topology Publications

Discussion in 'Math Research' started by Geometry and Topology, Sep 5, 2011.

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

    (1) Algebraic & Geometric Topology 11 (2011) 2237-2264
    Simplicial volume and fillings of hyperbolic manifolds
    by Koji Fujiwara and Jason Fox Manning
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p073.xhtml
    DOI: 10.2140/agt.2011.11.2237

    (2) Algebraic & Geometric Topology 11 (2011) 2265-2296
    The entropy efficiency of point-push mapping classes on the punctured disk
    by Philip Boyland and Jason Harrington
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p074.xhtml
    DOI: 10.2140/agt.2011.11.2265

    (3) Algebraic & Geometric Topology 11 (2011) 2297-2318
    Bounds for fixed points and fixed subgroups on surfaces and graphs
    by Boju Jiang, Shida Wang and Qiang Zhang
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p075.xhtml
    DOI: 10.2140/agt.2011.11.2297

    (4) Algebraic & Geometric Topology 11 (2011) 2319-2368
    Families of monotone symplectic manifolds constructed via
    symplectic cut and their Lagrangian submanifolds
    by Agnes Gadbled
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p076.xhtml
    DOI: 10.2140/agt.2011.11.2319

    (5) Algebraic & Geometric Topology 11 (2011) 2369-2390
    On the mapping space homotopy groups and the free loop space homology groups
    by Takahito Naito
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p077.xhtml
    DOI: 10.2140/agt.2011.11.2369
    `
    (6) Algebraic & Geometric Topology 11 (2011) 2391-2436
    Algebraic K-theory over the infinite dihedral group: an algebraic approach
    by James F Davis, Qayum Khan and Andrew Ranicki
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p078.xhtml
    DOI: 10.2140/agt.2011.11.2391

    (7) Algebraic & Geometric Topology 11 (2011) 2437-2452
    Free degrees of homeomorphisms on compact surfaces
    by Jianchun Wu and Xuezhi Zhao
    URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p079.xhtml
    DOI: 10.2140/agt.2011.11.2437

    One paper has been published by Geometry & Topology

    (8) Geometry & Topology 15 (2011) 1545-1567
    Free planar actions of the Klein bottle group
    by Frederic Le Roux
    URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p039.xhtml
    DOI: 10.2140/gt.2011.15.1545

    Abstracts follow

    (1) Simplicial volume and fillings of hyperbolic manifolds
    by Koji Fujiwara and Jason Fox Manning

    Let M be a hyperbolic n-manifold whose cusps have torus cross-
    sections. In an earlier paper, the authors constructed a variety of
    nonpositively and negatively curved spaces as "2pi-fillings" of M by
    replacing the cusps of M with compact "partial cones" of their
    boundaries. These 2pi-fillings are closed pseudomanifolds, and so
    have a fundamental class. We show that the simplicial volume of any
    such 2pi-filling is positive, and bounded above by Vol(M)/v_n, where
    v_n is the volume of a regular ideal hyperbolic n-simplex. This
    result generalizes the fact that hyperbolic Dehn filling of a
    3-manifold does not increase hyperbolic volume.

    In particular, we obtain information about the simplicial volumes of
    some 4-dimensional homology spheres described by Ratcliffe and
    Tschantz, answering a question of Belegradek and establishing the
    existence of 4-dimensional homology spheres with positive simplicial
    volume.


    (2) The entropy efficiency of point-push mapping classes on the punctured disk
    by Philip Boyland and Jason Harrington

    We study the maximal entropy per unit generator of point-push mapping
    classes on the punctured disk. Our work is motivated by fluid mixing
    by rods in a planar domain. If a single rod moves among N fixed
    obstacles, the resulting fluid diffeomorphism is in the point-push
    mapping class associated with the loop in the fundamental group of the
    N-punctured disk traversed by the single stirrer. The collection of
    motions where each stirrer goes around a single obstacle generate the
    group of point-push mapping classes, and the entropy efficiency with
    respect to these generators gives a topological measure of the mixing
    per unit energy expenditure of the mapping class. We give lower and
    upper bounds for Eff(N), the maximal efficiency in the presence of N
    obstacles, and prove that Eff(N) approaches log(3) as N tends to
    infinity. For the lower bound we compute the entropy efficiency of a
    specific point-push protocol, HSP_N, which we conjecture achieves the
    maximum. The entropy computation uses the action on chains in a
    Z-covering space of the punctured disk which is designed for
    point-push protocols. For the upper bound we estimate the exponential
    growth rate of the action of the point-push mapping classes on the
    fundamental group of the punctured disk using a collection of
    incidence matrices and then computing the generalized spectral radius
    of the collection.


    (3) Bounds for fixed points and fixed subgroups on surfaces and graphs
    by Boju Jiang, Shida Wang and Qiang Zhang

    We consider selfmaps of hyperbolic surfaces and graphs, and give some
    bounds involving the rank and the index of fixed point classes. One
    consequence is a rank bound for fixed subgroups of surface group
    endomorphisms, similar to the Bestvina-Handel bound (originally known
    as the Scott conjecture) for free group automorphisms.

    When the selfmap is homotopic to a homeomorphism, we rely on
    Thurston's classification of surface automorphisms. When the surface
    has boundary, we work with its spine, and Bestvina-Handel's theory of
    train track maps on graphs plays an essential role.

    It turns out that the control of empty fixed point classes (for
    surface automorphisms) presents a special challenge. For this
    purpose, an alternative definition of fixed point class is introduced,
    which avoids covering spaces hence is more convenient for geometric
    discussions.


    (4) Families of monotone symplectic manifolds constructed via
    symplectic cut and their Lagrangian submanifolds
    by Agnes Gadbled

    We describe families of monotone symplectic manifolds constructed via
    the symplectic cutting procedure of Lerman [Math. Res. Lett. 2 (1995)
    247--258] from the cotangent bundle of manifolds endowed with a free
    circle action. We also give obstructions to the monotone Lagrangian
    embedding of some compact manifolds in these symplectic manifolds.


    (5) On the mapping space homotopy groups and the free loop space homology groups
    by Takahito Naito

    Let X be a Poincare duality space, Y a space and f a based map from X
    to Y. We show that the rational homotopy group of the connected
    component of the space of maps from X to Y containing f is contained
    in the rational homology group of a space L_f Y which is the pullback
    of f and the evaluation map from the free loop space LY to the space
    Y. As an application of the result, when X is a closed oriented
    manifold, we give a condition of a noncommutativity for the rational
    loop homology algebra H_{*+d}(L_f Y;Q) defined by Gruher and Salvatore
    which is the extension of the Chas-Sullivan loop homology algebra.


    (6) Algebraic K-theory over the infinite dihedral group: an algebraic approach
    by James F Davis, Qayum Khan and Andrew Ranicki

    Two types of Nil-groups arise in the codimension 1 splitting
    obstruction theory for homotopy equivalences of finite CW--complexes:
    the Farrell--Bass Nil-groups in the nonseparating case when the
    fundamental group is an HNN extension and the Waldhausen Nil-groups in
    the separating case when the fundamental group is an amalgamated free
    product. We obtain a general Nil-Nil theorem in algebraic K-theory
    relating the two types of Nil-groups.

    The infinite dihedral group is a free product and has an index 2
    subgroup which is an HNN extension, so both cases arise if the
    fundamental group surjects onto the infinite dihedral group. The
    Nil-Nil theorem implies that the two types of the reduced
    tilde-Nil-groups arising from such a fundamental group are isomorphic.
    There is also a topological application: in the finite-index case of
    an amalgamated free product, a homotopy equivalence of finite
    CW-complexes is semisplit along a separating subcomplex.


    (7) Free degrees of homeomorphisms on compact surfaces
    by Jianchun Wu and Xuezhi Zhao

    For a compact surface M, the free degree fr(M) of homeomorphisms on M
    is the minimum positive integer n with property that for any self
    homeomorphism xi of M, at least one of the iterates xi,xi^2,...,xi^n
    has a fixed point. This is to say fr(M) is the maximum of least
    periods among all periodic points of self homeomorphisms on M. We
    prove that fr(F_{g,b}) is at most 24g-24 for g at least 2 and
    fr(N_{g,b}) is at most 12g-24 for g at least 3.


    (8) Free planar actions of the Klein bottle group
    by Frederic Le Roux

    We describe the structure of the free actions of the fundamental group
    of the Klein bottle <a,b|aba^{-1}=b^{-1}> by orientation preserving
    homeomorphisms of the plane. The main result is that a must act
    properly discontinuously, while b cannot act properly discontinuously.
    As a corollary, we describe some torsion free groups that may not act
    freely on the plane. We also find some properties which are
    reminiscent of Brouwer theory for the integers, in particular that
    every free action is virtually wandering.



    Geometry & Topology Publications is an imprint of
    Mathematical Sciences Publishers
     
    Geometry and Topology, Sep 5, 2011
    #1
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