Homotopy types of stabilizers and orbits of Morse functions on surfaces
| dc.creator | Maksymenko, Sergey | |
| dc.date | 2003-10-06 | |
| dc.date | 2006-08-14 | |
| dc.date.accessioned | 2026-07-07T06:35:45Z | |
| dc.date.available | 2026-07-07T06:35:45Z | |
| dc.description | Let $M$ be a smooth compact surface, orientable or not, with boundary or without it, $P$ either the real line $R^1$ or the circle $S^1$, and $Diff(M)$ the group of diffeomorphisms of $M$ acting on $C^{\infty}(M,P)$ by the rule $h\cdot f\mapsto f \circ h^{-1}$, where $h\in Diff(M)$ and $f \in C^{\infty}(M,P)$. Let $f:M \to P$ be a Morse function and $O(f)$ be the orbit of $f$ under this action. We prove that $π_k O(f)=π_k M$ for $k\geq 3$, and $π_2 O(f)=0$ except for few cases. In particular, $O(f)$ is aspherical, provided so is $M$. Moreover, $π_1 O(f)$ is an extension of a finitely generated free abelian group with a (finite) subgroup of the group of automorphisms of the Reeb graph of $f$. We also give a complete proof of the fact that the orbit $O(f)$ is tame Frechet submanifold of $C^{\infty}(M,P)$ of finite codimension, and that the projection $Diff(M) \to O(f)$ is a principal locally trivial $S(f)$-fibration. | |
| dc.description | 49 pages, 8 figures. This version includes the proof of the fact that the orbits of a finite codimension of tame action of tame Lie group on tame Frechet manifold is a tame Frechet manifold itself | |
| dc.identifier | https://arxiv.org/abs/math/0310067 | |
| dc.identifier | http://arxiv.org/abs/math/0310067 | |
| dc.identifier | Annals of Global Analysis and Geometry 29 (2006) 241-285 | |
| dc.identifier | doi:10.1007/s10455-005-9012-6 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99885 | |
| dc.subject | Geometric Topology | |
| dc.subject | Functional Analysis | |
| dc.subject | 46M18, 46E15, 57S25, 57M50, 37E35 | |
| dc.title | Homotopy types of stabilizers and orbits of Morse functions on surfaces | |
| dc.type | text |