arXiv 0806.47042008-06math.GTmath.AT

Functions with isolated singularities on surfaces

Sergiy Maksymenko

备注：: 46 pages, 10 figures. v2. The paper is essentially rewritten and extended to new types of singularities. Due to the increased length, the last part of version 1 concerning reduction of calculations of the fundamental groups of orbits will be moved to another paper

英文摘要：

Let M be a smooth connected compact surface, P be either the real line R^1 or the circle S^1, and f:M-->P be a smooth mapping. In a previous series of papers for the case when f is a Morse map the author calculated the homotopy types of stabilizers and orbits of f with respect to the right action of the diffeomorphisms group of M. The present paper extends those calculations to a large class of maps M-->P with degenerate singularities satisfying certain set of axioms.

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