Mathematics – Geometric Topology
Scientific paper
2008-11-25
Mathematics
Geometric Topology
19 pages, 4 figures
Scientific paper
In this paper we consider the realization of DE attractors by self-diffeomorphisms of manifolds. For any expanding self-map $\phi:M\to M$ of a connected, closed $p$-dimensional manifold $M$, one can always realize a $(p,q)$-type attractor derived from $\phi$ by a compactly-supported self-diffeomorphsm of $\RR^{p+q}$, as long as $q\geq p+1$. Thus lower codimensional realizations are more interesting, related to the knotting problem below the stable range. We show that for any expanding self-map $\phi$ of a standard smooth $p$-dimensional torus $T^p$, there is compactly-supported self-diffeomorphism of $\RR^{p+2}$ realizing an attractor derived from $\phi$. A key ingredient of the construction is to understand automorphisms of $T^p$ which extend over $\RR^{p+2}$ as a self-diffeomorphism via the standard unknotted embedding $\imath_p:T^p\hookrightarrow\RR^{p+2}$. We show that these automorphisms form a subgroup $E_{\imath_p}$ of $\Aut(T^p)$ of index at most $2^p-1$.
Ding Fan
Liu Yi
Wang Shicheng
Yao Jiangang
No associations
LandOfFree
Extending $T^p$ automorphisms over $\RR^{p+2}$ and realizing DE attractors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Extending $T^p$ automorphisms over $\RR^{p+2}$ and realizing DE attractors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extending $T^p$ automorphisms over $\RR^{p+2}$ and realizing DE attractors will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-304177