Real loci of symplectic reductions |
| |
Authors: | R. F. Goldin T. S. Holm |
| |
Affiliation: | Mathematical Sciences, George Mason University, MS 3F2, 4400 University Dr., Fairfax, Virgina 22030 ; Department of Mathematics, University of California Berkeley, 813 Evans Hall, Berkeley, California 94720 |
| |
Abstract: | Let be a compact, connected symplectic manifold with a Hamiltonian action of a compact -dimensional torus . Suppose that is equipped with an anti-symplectic involution compatible with the -action. The real locus of is the fixed point set of . Duistermaat introduced real loci, and extended several theorems of symplectic geometry to real loci. In this paper, we extend another classical result of symplectic geometry to real loci: the Kirwan surjectivity theorem. In addition, we compute the kernel of the real Kirwan map. These results are direct consequences of techniques introduced by Tolman and Weitsman. In some examples, these results allow us to show that a symplectic reduction has the same ordinary cohomology as its real locus , with degrees halved. This extends Duistermaat's original result on real loci to a case in which there is not a natural Hamiltonian torus action. |
| |
Keywords: | Real locus symplectic reduction |
|
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 |
|
点击此处可从《Transactions of the American Mathematical Society》下载全文 |
|