Stabilizers and orbits of circle-valued smooth functions

Details Stabilizers and orbits of circle-valued smooth functions Stabilizers and orbits of circle-valued smooth functions

2005-03-31

arxiv.org/abs/math/0503734v1

Mathematics

Functional Analysis

11 pages, 1 figure. This paper is an extension of author's preprint http://xxx.lanl.gov/math.FA/0411612 to circle-valued funct

Scientific paper

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 $O_{MS} \sim O_M \times S^1$.

Affiliated with

Also associated with

No associations

Rating

Stabilizers and orbits of circle-valued smooth functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stabilizers and orbits of circle-valued smooth functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stabilizers and orbits of circle-valued smooth functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-721042