Homotopy type of stabilizers of smooth functions with non-isolated singularities on surfaces

2023/05/14 by Bohdan Feshchenko, Feshchenko, Bohdan
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2305.08255

openalex publication_date 2023/05/14 · openalex created_date 2023/05/17 · openalex updated_date 2026/07/28

Abstract

The paper is devoted to the study of homotopy properties of stabilizers of smooth functions on oriented surfaces, i.e., groups of diffeomorphisms of surfaces preserving a given function. For some class of smooth functions which is a generalization of the class of Morse-Bott functions on oriented surfaces, the homotopy type of the connected component of the identity map of the stabilizer is completely described.

Related

• Functions with isolated singularities on surfaces
• Functions with isolated singularities on surfaces, II
• Structure of the fundamental groups of orbits of smooth functions on surfaces
• Homotopy properties of smooth functions on the Möbius band
• Homological stability for quotients of mapping class groups of surfaces by the Johnson subgroups