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Yi Liu

  1. A spin obstruction for codimension-two diffeomorphism and homeomorphism extension.

    Втр, 10/27/2009 - 16:01 — SomNambul
    Authors: Fan Ding, Shicheng Wang, Jiangang Yao, Yi Liu
    Subjects: Geometric Topology
    Abstract

    Let $\imath: M^p\to \RR^{p+2}$ be a codimension-2 smooth embedding from
    closed orientable manifold to the Euclidean space, then there is a spin
    structure $\imath^#(\varsigma^{p+2})$ on $M$ canonically induced from the
    embedding. If an orientation-preserving self-diffeomorphism $\tau$ of $M$
    extends over $\imath$ as an orientation-preserving self-homeomorphism of
    $\RR^{p+2}$, then $\tau$ preserves the induced spin structure.

  2. Extending $T^p$ automorphisms over $\RR^{p+2}$ and realizing DE attractors.

    Втр, 09/08/2009 - 12:16 — SomNambul
    Authors: Fan Ding, Shicheng Wang, Jiangang Yao, Yi Liu
    Subjects: Geometric Topology
    Abstract

    We show that for any expanding map $\phi: T^p\to T^p$, there is an
    orientation-preserving self-diffeomorphism of $\RR^{p+2}$ realizing a
    hyperbolic attractor derived from $\phi$. The construction is based on a result
    in differential topology that for the standard unknotted embedding
    $\imath_p:T^p\to\RR^{p+2}$, the subgroup $E_{\imath_p}$ of
    $\Aut(T^p)\cong\SL(p,\ZZ)$ which consists of automorphisms that extend over
    $\RR^{p+2}$ as orientation-preserving diffeomorphisms, has index at most
    $2^p-1$.

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