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Ukrainian Mathematical Journal

, Volume 64, Issue 9, pp 1350–1369 | Cite as

Homotopic types of right stabilizers and orbits of smooth functions on surfaces

  • S. I. Maksimenko
Article
  • 35 Downloads

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 XM, 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:MP with isolated singularities containing all Morse mappings. For each mapping f\( \mathcal{F} \), we consider certain submanifolds XM “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.

Keywords

Smooth Function Exact Sequence Mapping Class Group Morse Function Regular Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • S. I. Maksimenko
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKievUkraine

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