English

Functions with isolated singularities on surfaces

Geometric Topology 2009-12-17 v2 Algebraic Topology

Abstract

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.

Keywords

Cite

@article{arxiv.0806.4704,
  title  = {Functions with isolated singularities on surfaces},
  author = {Sergiy Maksymenko},
  journal= {arXiv preprint arXiv:0806.4704},
  year   = {2009}
}

Comments

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

R2 v1 2026-06-21T10:55:25.763Z