Deformations of circle-valued Morse functions on surfaces
Let M be a smooth connected orientable compact surface and let Fcov(M,S1) be a space of all Morse functions f : M → S₁ without critical points on ∂M such that, for any connected component V of ∂M, the restriction f : V → S₁ is either a constant map or a covering map. The space Fcov(M,S₁) is endowed...
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| Datum: | 2010 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2010
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| Schriftenreihe: | Український математичний журнал |
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/166305 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Deformations of circle-valued Morse functions on surfaces / S.I. Maksymenko // Український математичний журнал. — 2010. — Т. 62, № 10. — С. 1360–1366. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Let M be a smooth connected orientable compact surface and let Fcov(M,S1) be a space of all Morse functions f : M → S₁ without critical points on ∂M such that, for any connected component V of ∂M, the restriction f : V → S₁ is either a constant map or a covering map. The space Fcov(M,S₁) is endowed with the C ∞-topology. We present the classification of connected components of the space Fcov(M,S₁). 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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