Functions with isolated singularities on surfaces

2008/06/28 by Maksymenko, Sergiy · 1 citation
#37C05 #57R45 #57S05 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0806.4704

Abstract

Let M be a smooth connected compact surface, P be either the real line R¹ or the circle S¹, 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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