Deformations of circle-valued Morse functions on surfaces

Details Deformations of circle-valued Morse functions on surfaces Deformations of circle-valued Morse functions on surfaces

2010-06-09

arxiv.org/abs/1006.1708v1

Mathematics

Geometric Topology

8 pages, 4 figures

Scientific paper

Let M be a smooth connected orientable compact surface. Denote by F(M,S^1) the space of all Morse functions f:M-->S^1 having no critical points on the boundary of M and such that for every boundary component V of M, the restriction f|V:V-->S^1 is either a constant map or a covering map. Endow F(M,S^1) with the C^{\infty}-topology. In this note the connected components of F(M,S^1) are classified. This result extends the results of S.V.Matveev, V.V.Sharko, and the author for the case of Morse functions being locally constant on the boundary of M.

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