Normal forms of functions with degenerate singularities on surfaces equipped with semi-free circle actions

2024/12/25 by Feshchenko, Bohdan · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2412.18944

Abstract

This article is devoted to the study of a certain class of smooth circle-valued functions on a cylinder S¹× [0,1], a torus T², a disk D² and a sphere S² which is a generalization of Morse-Bott functions without saddles. We established a "normal form" for functions from this class, namely, we proved that any such function f can be presented in the form f = \varkappa∘ f₀∘ h^-1, where f₀ is the ``simplest'' Morse function on the given surface for some diffeomorphism h and a smooth function \varkappa satisfying some natural conditions.

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