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James W. Anderson

  1. Prising apart geodesics by length in hyperbolic 3-manifolds.

    Tue, 02/07/2012 - 15:01 — SomNambul
    Authors: James W. Anderson
    Subjects: Geometric Topology
    Abstract

    In this note, we develop a condition on a closed curve on a surface or in a
    3-manifold that implies that the curve has the property that its length
    function on the space of all hyperbolic structures on the surface or 3-manifold
    completely determines the curve.

  2. Strong convergence of Kleinian groups: the cracked eggshell.

    Wed, 03/10/2010 - 16:01 — SomNambul
    Authors: James W. Anderson, Cyril Lecuire
    Subjects: Geometric Topology
    Abstract

    In this paper we give a complete description of the set of discrete faithful
    representations SH(M) uniformizing a compact, orientable, hyperbolizable
    3-manifold M with incompressible boundary, equipped with the strong topology,
    with the description given in term of the end invariants of the quotient
    manifolds. As part of this description, we introduce coordinates on SH(M) that
    extend the usual Ahlfors-Bers coordinates. We use these coordinates to show the
    local connectivity of SH(M) and study the action of the modular group of M on
    SH(M).

  3. Small filling sets of curves on a surface.

    Fri, 09/11/2009 - 19:12 — SomNambul
    Authors: James W. Anderson, Hugo Parlier, Alexandra Pettet
    Subjects: Geometric Topology
    Abstract

    Consider a set of simple closed curves on a surface of genus $g$ which fill
    the surface and which pairwise intersect at most once. We show that the
    asymptotic growth rate of the smallest number in such a set is $2\sqrt{g}$ as
    $g \to \infty$. More generally, we give a precise asymptotic for filling sets
    of curves which pairwise intersect at most $K \geq 1$ times. We then bound from
    below the cardinality of a filling set of {\it systoles} by
    $\frac{g}{\log(g)}$.

  4. Small filling sets of curves on a surface.

    Fri, 09/11/2009 - 19:12 — SomNambul
    Authors: James W. Anderson, Hugo Parlier, Alexandra Pettet
    Subjects: Geometric Topology
    Abstract

    Consider a set of simple closed curves on a surface of genus $g$ which fill
    the surface and which pairwise intersect at most once. We show that the
    asymptotic growth rate of the smallest number in such a set is $2\sqrt{g}$ as
    $g \to \infty$. More generally, we give a precise asymptotic for filling sets
    of curves which pairwise intersect at most $K \geq 1$ times. We then bound from
    below the cardinality of a filling set of {\it systoles} by
    $\frac{g}{\log(g)}$.

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