A Convexity Theorem and Reduced Delzant Spaces
| dc.creator | Lian, Bong H. | |
| dc.creator | Song, Bailin | |
| dc.date | 2005-09-19 | |
| dc.date | 2007-02-27 | |
| dc.date.accessioned | 2026-07-07T07:48:45Z | |
| dc.date.available | 2026-07-07T07:48:45Z | |
| dc.description | The convexity theorem of Atiyah and Guillemin-Sternberg says that any connected compact manifold with Hamiltonian torus action has a moment map whose image is the convex hull of the image of the fixed point set. Sjamaar-Lerman proved that the Marsden-Weinstein reduction of a connected Hamitonian $G$-manifold is a stratified symplectic space. Suppose $1\ra A\ra G\ra T\ra 1$ is an exact sequence of compact Lie groups and $T$ is a torus. Then the reduction of a Hamiltonian $G$-manifold with respect to $A$ yields a Hamiltonian $T$-space. We show that if the $A$-moment map is proper, then the convexity theorem holds for such a Hamiltonian $T$-space, even when it is singular. We also prove that if, furthermore, the $T$-space has dimension $2dim T$ and $T$ acts effectively, then the moment polytope is sufficient to essentially distinguish their homeomorphism type, though not their diffeomorphism types. This generalizes a theorem of Delzant in the smooth case. | |
| dc.description | 43 pages; a few corrections made | |
| dc.identifier | https://arxiv.org/abs/math/0509429 | |
| dc.identifier | http://arxiv.org/abs/math/0509429 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124611 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 53D20 (Primary); 14M25 (Secondary) | |
| dc.title | A Convexity Theorem and Reduced Delzant Spaces | |
| dc.type | text |