Deformations of smooth functions on 2-torus

2019/03/05 by Feshchenko, Bohdan · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1903.01753

Abstract

Let f be a Morse function on a smooth compact surface M and S'(f) be a group of f-preserving diffeomorphisms of M which are isotopic to the identity map. Let also G(f) be a group of automorphisms of the graph of f induced by elements from S'(f), and Δ' be a subgroup of S'(f) of diffeomorphisms which trivially act on the graph of f and are isotopic to the identity map. The group π₀S'(f) can be viewed as an analogue of a mapping class group for f-preserved diffeomorphisms of M. Groups π₀Δ'(f) and G(f) can be viewed as groups which encode `combinatorially trivial' and `combinatorially nontrivial' counterparts of π₀S'(f) respectively. In the paper we compute groups π₀S'(f), G(f), and π₀Δ'(f) for Morse functions on 2-torus T².

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