Deformations of circle-valued Morse functions on surfaces
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 m...
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| Date: | 2010 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2010
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2960 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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 $∂M$. |
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