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Peter Teichner

  1. Whitney tower concordance of classical links.

    Fri, 02/17/2012 - 15:01 — SomNambul
    Authors: James Conant, Rob Schneiderman, Peter Teichner
    Subjects: Geometric Topology
    Abstract

    This paper computes Whitney tower filtrations of classical links. Whitney
    towers consist of iterated stages of Whitney disks and allow a tree-valued
    intersection theory, showing that the associated graded quotients of the
    filtration are finitely generated abelian groups. Twisted Whitney towers are
    studied and a new quadratic refinement of the intersection theory is
    introduced, measuring Whitney disk framing obstructions.

  2. Universal Quadratic Forms and Untwisting Whitney Towers.

    Wed, 01/19/2011 - 16:01 — SomNambul
    Authors: James Conant, Rob Schneiderman, Peter Teichner
    Subjects: Geometric Topology
    Abstract

    The first part of this paper completes the classification of Whitney towers
    in the 4-ball that was started in three related papers. We provide an algebraic
    framework allowing the computations of the graded groups associated to
    geometric filtrations of classical link concordance by order $n$ (twisted)
    Whitney towers in the 4-ball. Higher-order Sato-Levine invariants and
    higher-order Arf invariants are defined and shown to be the obstructions to
    framing a twisted Whitney tower.

  3. Geometric Filtrations of Classical Link Concordance.

    Wed, 01/19/2011 - 16:01 — SomNambul
    Authors: James Conant, Rob Schneiderman, Peter Teichner
    Subjects: Geometric Topology
    Abstract

    This paper describes grope and Whitney tower filtrations on the set of
    concordance classes of classical links in terms of class and order
    respectively. Using the tree-valued intersection theory of Whitney towers, the
    associated graded quotients are shown to be finitely generated abelian groups
    under a (surprisingly) well-defined connected sum operation. Twisted Whitney
    towers are also introduced, along with a corresponding quadratic enhancement of
    the intersection theory for framed Whitney towers that measures Whitney-disk
    framing obstructions.

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