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28 March 2024
 
  » arxiv » 1409.0502

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Orbits of smooth functions on 2-torus and their homotopy types
Sergiy Maksymenko ; Bohdan Feshchenko ;
Date 1 Sep 2014
AbstractLet $f:T^2 omathbb{R}$ be a Morse function on $2$-torus $T^2$ such that its Kronrod-Reeb graph $Gamma(f)$ has exactly one cycle, i.e. it is homotopy equivalent to $S^1$. Under some additional conditions we describe a homotopy type of the orbit of $f$ with respect to the action of the group of diffeomorphism of $T^2$.
This result holds for a larger class of smooth functions $f:T^2 omathbb{R}$ having the following property: for every critical point $z$ of $f$ the germ of $f$ at $z$ is smoothly equivalent to a homogeneous polynomial $mathbb{R}^2 omathbb{R}$ without multiple factors.
Source arXiv, 1409.0502
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