Path-components of Morse mappings spaces of surfaces

• Autores: Sergey Maksymenko
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 80, Nº 3, 2005, págs. 655-690
• Idioma: inglés
• DOI: 10.4171/cmh/30
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• Resumen

  • Let $M$ be a connected compact surface, $P$ be either ${\Bbb R}^1$ or $S^1$, and ${\cal F}(M,P)$ be the space of Morse mappings $M\to P$ with compact-open topology. The classification of path-components of ${\cal F}(M,P)$ was independently obtained by S. V. Matveev and V. V. Sharko for the case $P={\Bbb R}^1$, and by the author for orientable surfaces and $P=S^1$. In this paper we give a new independent and unified proof of this classification for all compact surfaces in the case $P=P={\Bbb R}$, and for orientable surfaces in the case $P=S^1$. We also extend the author's initial proof to non-orientable surfaces