Homotopy dimension of orbits of Morse functions on surfaces

Details Homotopy dimension of orbits of Morse functions on surfaces Homotopy dimension of orbits of Morse functions on surfaces

2007-10-24

arxiv.org/abs/0710.4437v2

Mathematics

Algebraic Topology

Submitted to the Proceedings of the 8th Conference on Geometry and Topology of Manifolds, 6 pages

Scientific paper

Let f be a real- or circle-valued Morse function on a compact surface M having exactly n>0 critical points. Denote by O the orbit of f with respect to the right action of the group of diffeomorphisms of M. We show that the connected components of O have the homotopy type of a finite-dimensional CW-complex. Actually, these connected components are homotopy equivalent to a certain covering space of the n-th configuration space of the interior of M. As a consequence we obtain that the fundamental group of O is a subgroup of the n-th braid group of M.

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