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Article overview
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Orbits of smooth functions on 2-torus and their homotopy types | Sergiy Maksymenko
; Bohdan Feshchenko
; | Date: |
1 Sep 2014 | Abstract: | Let $f:T^2 omathbb{R}$ 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 | Services: | Forum | Review | PDF | Favorites |
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