On nearly semifree circle actions
| dc.creator | McDuff, Dusa | |
| dc.creator | Tolman, Susan | |
| dc.date | 2005-03-22 | |
| dc.date.accessioned | 2026-07-07T05:18:14Z | |
| dc.date.available | 2026-07-07T05:18:14Z | |
| dc.description | 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 $π_1(G)$ may be represented by a semifree $S^1$-action. A theorem of McDuff--Slimowitz then implies that $π_1(G)$ injects into $π_1(\Ham(M, \om))$, 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 $(M,ω)$ 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 $G$ | |
| dc.description | This paper used to be part of SG/0404338 | |
| dc.identifier | https://arxiv.org/abs/math/0503467 | |
| dc.identifier | http://arxiv.org/abs/math/0503467 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74591 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Group Theory | |
| dc.subject | Primary 53D05, Secondary 22E46 | |
| dc.title | On nearly semifree circle actions | |
| dc.type | text |