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arXiv · 1006.1708

Deformations of circle-valued Morse functions on surfaces

Sergiy Maksymenko
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Abstract

Let $M$ be a smooth connected orientable compact surface. Denote by $F(M,S^1)$ the space of all Morse functions $f:M\to S^1$ having no critical points on the boundary of $M$ and such that for every boundary component $V$ of $M$ the restriction $f|_{V}:V\to S^1$ 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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Sergiy Maksymenko. 2015-12-24. Deformations of circle-valued Morse functions on surfaces. https://doi.org/10.1007/s11253-011-0450-y

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