Stabilizers and orbits of circle-valued smooth functions
| dc.creator | Maksymenko, Sergey | |
| dc.date | 2005-03-31 | |
| dc.date.accessioned | 2026-07-07T05:18:40Z | |
| dc.date.available | 2026-07-07T05:18:40Z | |
| dc.description | Let $M$ be a smooth compact manifold and $P$ be either $R^1$ or $S^1$. There is a natural action of the groups $Diff(M)$ and $Diff(M) \times Diff(P)$ on the space of smooth mappings $C^{\infty}(M,P)$. For $f\in C^{\infty}(M,P)$ let $S_f$, $S_{MP}$, $O_f$, and $O_{MP}$ be the stabilizers and orbits of $f$ under these actions. Recently, the author proved that under mild conditions on $f\in C^{\infty}(M,R^1)$ the corresponding stabilizers and orbits are homotopy equivalent: $S_{MR} \sim S_{M}$ and $O_{MR} \sim O_M$. These results are extended here to the actions on $C^{\infty}(M,S^1)$. It is proved that under the similar conditions (that are rather typical) we have that $S_{MS}\sim S_M$ and $O_{MS} \sim O_M \times S^1$. | |
| dc.description | 11 pages, 1 figure. This paper is an extension of author's preprint http://xxx.lanl.gov/math.FA/0411612 to circle-valued functions | |
| dc.identifier | https://arxiv.org/abs/math/0503734 | |
| dc.identifier | http://arxiv.org/abs/math/0503734 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74744 | |
| dc.subject | Functional Analysis | |
| dc.subject | Algebraic Topology | |
| dc.subject | Dynamical Systems | |
| dc.subject | Geometric Topology | |
| dc.subject | 58K05; 14H40 | |
| dc.title | Stabilizers and orbits of circle-valued smooth functions | |
| dc.type | text |