Homotopic types of right stabilizers and orbits of smooth functions on surfaces
| Autor: | S. I. Maksimenko |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Ukrainian Mathematical Journal. 64:1350-1369 |
| ISSN: | 1573-9376 0041-5995 |
| DOI: | 10.1007/s11253-013-0721-x |
| Popis: | Let M be a connected smooth compact surface and let P be either the number line $$ \mathbb{R} $$ or a circle S 1. For a subset X ⊂ M, by $$ \mathcal{D} $$ (M, X) we denote a group of diffeomorphisms of M fixed on X. We consider a special class $$ \mathcal{F} $$ of smooth mappings f:M → P with isolated singularities containing all Morse mappings. For each mapping f ∈ $$ \mathcal{F} $$ , we consider certain submanifolds X ⊂ M “adapted” to f in a natural way and study the right action of the group $$ \mathcal{D} $$ (M, X) on C ∞( M, P). The main results of the paper describe the homotopic types of the connected components of stabilizers $$ \mathcal{S} $$ (f) and the orbits $$ \mathcal{O} $$ (f) of all mappings f ∈ $$ \mathcal{F} $$ and generalize the results of the author in this field obtained earlier. |
| Databáze: | OpenAIRE |
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