Smooth shifts along flows

2001/06/30 by Sergey Maksymenko
Mathematics · #math.GT #math.AT #math.FA #msc:58D05 #msc:58D15 #msc:57S05 #msc:46T10

paper · pdf

published as Topology and Applications, 130 (2003) 183-204 · 25 pages, final version

arxiv created 2004/07/07 · arxiv updated 2009/11/30

Abstract

Let Φ be a flow on a smooth, compact, finite-dimensional manifold M. Consider the subsets E(Φ) and D(Φ) of C^∞(M,M) consisting of smoothh mappings and diffeomorphisms (respectively) of M preserving the foliation of the flow Φ. Let also E₀(Φ) and D₀(Φ) be the identity path components of E(Φ) and D(Φ) with compact-open topology. We prove that under mild conditions on fixed points of Φ the inclusion D₀(Φ) ⊂ E₀(Φ) is a homotopy equivalence and these spaces are either contractible or homotopically equivalent to the circle.

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