2017
Том 69
№ 6

All Issues

Deformations of circle-valued Morse functions on surfaces

Maksimenko S. I.

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Abstract

Let $M$ be a smooth connected orientable compact surface and let $\mathcal{F}_{\text{cov}}(M,S^1)$ be a space of all Morse functions $f: M → S^1$ without critical points on $∂M$ such that, for any connected component $V$ of $∂M$, the restriction $f : V → S^1$ is either a constant map or a covering map. The space $\mathcal{F}_{\text{cov}}(M,S^1)$ is endowed with the $C^{∞}$-topology. We present the classification of connected components of the space $\mathcal{F}_{\text{cov}}(M,S^1)$. This result generalizes the results obtained by Matveev, Sharko, and the author for the case of Morse functions locally constant on $∂M$.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 10, pp 1577-1584.

Citation Example: Maksimenko S. I. Deformations of circle-valued Morse functions on surfaces // Ukr. Mat. Zh. - 2010. - 62, № 10. - pp. 1360–1366.

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