On nearly semifree circle actions

Details On nearly semifree circle actions On nearly semifree circle actions

2005-03-22

arxiv.org/abs/math/0503467v1

Mathematics

Symplectic Geometry

This paper used to be part of SG/0404338

Scientific paper

Recall that an effective circle action is semifree if the stabilizer subgroup of each point is connected. We show that if $(M, \om)$ is a coadjoint orbit of a compact Lie group $G$ then every element of $\pi_1(G)$ may be represented by a semifree $S^1$-action. A theorem of McDuff--Slimowitz then implies that $\pi_1(G)$ injects into $\pi_1(\Ham(M, \om))$, which answers a question raised by Weinstein. We also show that a circle action on a manifold $M$ which is semifree near a fixed point $x$ cannot contract in a compact Lie subgroup $G$ of the diffeomorphism group unless the action is reversed by an element of $G$ that fixes the point $x$. Similarly, if a circle acts in a Hamiltonian fashion on a manifold $(M,\omega)$ and the stabilizer of every point has at most two components, then the circle cannot contract in a compact Lie subgroup of the group of Hamiltonian symplectomorphism unless the circle is reversed by an element of $G$

Affiliated with

Also associated with

No associations

Rating

On nearly semifree circle actions 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 nearly semifree circle actions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On nearly semifree circle actions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-684559