Jiangang Yao
A spin obstruction for codimension-two diffeomorphism and homeomorphism extension.
Втр, 10/27/2009 - 16:01 — SomNambulAuthors: Fan Ding, Shicheng Wang, Jiangang Yao, Yi Liu
Subjects: Geometric Topology
AbstractLet $\imath: M^p\to \RR^{p+2}$ 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.- Читать далее
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Only rational homology spheres admit $\Omega(f)$ to be union of DE attractors.
Втр, 09/08/2009 - 12:16 — SomNambulAuthors: Fan Ding, Jianzhong Pan, Shicheng Wang, Jiangang Yao
Subjects: Geometric Topology
AbstractIf there exists a diffeomorphism $f$ on a closed, orientable $n$-manifold $M$
such that the non-wandering set $\Omega(f)$ consists of finitely many
orientable $(\pm)$ attractors derived from expanding maps, then $M$ must be a
rational homology sphere; moreover all those attractors are of topological
dimension $n-2$.Expanding maps are expanding on (co)homologies.
Extending $T^p$ automorphisms over $\RR^{p+2}$ and realizing DE attractors.
Втр, 09/08/2009 - 12:16 — SomNambulAuthors: Fan Ding, Shicheng Wang, Jiangang Yao, Yi Liu
Subjects: Geometric Topology
AbstractWe 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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