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Daniel S. Silver

  1. Knot Groups with Many Killers.

    Fri, 09/18/2009 - 11:36 — SomNambul
    Authors: Daniel S. Silver, Susan G. Williams, Wilbur Whitten
    Subjects: Geometric Topology
    Abstract

    The group of any nontrivial torus knot, hyperbolic 2-bridge knot, or
    hyperbolic knot with unknotting number one contains infinitely many elements,
    none the automorphic image of another, such that each normally generates the
    group.

  2. On a Theorem of Burde and de Rham.

    Tue, 08/18/2009 - 11:53 — SomNambul
    Authors: Daniel S. Silver, Susan G. Williams
    Subjects: Geometric Topology
    Abstract

    We generalize a theorem of Burde and de Rham characterizing the zeros of the
    Alexander polynomial. Given a representation of a knot group $\pi$, we define
    an extension of $\pi$, the Crowell group. For any GL(n,C) representation of
    $\pi$, the zeros of the associated twisted Alexander polynomial correspond to
    representations of the Crowell group into the group of dilations of C^n.

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