On polar foliations and fundamental group

Details On polar foliations and fundamental group On polar foliations and fundamental group

2010-12-04

arxiv.org/abs/1012.0926v2

Results in Mathematics: Volume 60, Issue 1 (2011), Page 213-223. The final publication is available at springerlink.com http

Mathematics

Differential Geometry

short version, 9 pages

Scientific paper

10.1007/s00025-011-0171-4

In this work we investigate the relation between the fundamental group of a complete Riemannian manifold $M$ and the quotient between the Weyl group and reflection group of a polar action on $M$, as well as the relation between the fundamental group of $M$ and the quotient between the lifted Weyl group and lifted reflection group. As applications we give short alternative proofs of two results. The first one, due to the author and T\"{o}ben, states that there is non-exceptional orbit, if $M$ is simply connected. The second result, due to Lytchak, states that the orbits are closed and embedded if $M$ is simply connected. All results are proved in the more general case of polar foliations.

Affiliated with

Also associated with

No associations

Rating

On polar foliations and fundamental group 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 On polar foliations and fundamental group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On polar foliations and fundamental group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-99647