Smooth shifts along flows

Details Smooth shifts along flows Smooth shifts along flows

2001-06-24

arxiv.org/abs/math/0106199v2

Topology and Applications, 130 (2003) 183-204

Mathematics

Geometric Topology

25 pages, final version

Scientific paper

Let $\Phi$ be a flow on a smooth, compact, finite-dimensional manifold $M$. Consider the subsets $E(\Phi)$ and $D(\Phi)$ of $C^{\infty}(M,M)$ consisting of smoothh mappings and diffeomorphisms (respectively) of $M$ preserving the foliation of the flow $\Phi$. Let also $E_{0}(\Phi)$ and $D_{0}(\Phi)$ be the identity path components of $E(\Phi)$ and $D(\Phi)$ with compact-open topology. We prove that under mild conditions on fixed points of $\Phi$ the inclusion $D_{0}(\Phi) \subset E_{0}(\Phi)$ is a homotopy equivalence and these spaces are either contractible or homotopically equivalent to the circle.

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