Topology of the spaces of functions with prescribed singularities on surfaces

Abstract

Let $M$ be a smooth connected orientable closed surface and $f_0\in C^{\infty }(M)$ a function having only critical points of the $A_{\mu }$-types, $\mu \in \mathbb{N}$. Let $\mathcal{F}=\mathcal{F}(f_0)$ be the set of functions $f\in C^{\infty }(M)$ having the same types of local singularities as those of $f_0$. We describe the homotopy type of the space $\mathcal{F}$, endowed with the $C^{\infty }$-topology, and its decomposition into orbits of the action of the group of "left-right changings of coordinates".

7 pages

References in corpus (2)

• Homotopy types of stabilizers and orbits of Morse functions on surfaces
• Topology of the spaces of functions with prescribed singularities on surfaces

Cited by in corpus (4)

• Topology of the spaces of functions with prescribed singularities on surfaces
• Homotopy types of diffeomorphism groups of polar Morse-Bott foliations on lens spaces, 1
• Topological actions of wreath products
• Topology of spaces of smooth functions and gradient-like flows with prescribed singularities on surfaces