Localization theorems by symplectic cuts
| dc.creator | Jeffrey, Lisa | |
| dc.creator | Kogan, Mikhail | |
| dc.date | 2003-10-15 | |
| dc.date.accessioned | 2026-07-07T05:01:55Z | |
| dc.date.available | 2026-07-07T05:01:55Z | |
| dc.description | Given a compact symplectic manifold M with the Hamiltonian action of a torus T, let zero be a regular value of the moment map, and M_0 the symplectic reduction at zero. Denote by κ_0 the Kirwan map H^*_T(M)-> H^*(M_0). For an equivariant cohomology class η\in H^*_T(M) we present new localization formulas which express \int_{M_0} κ_0(η) as sums of certain integrals over the connected components of the fixed point set M^T. To produce such a formula we apply a residue operation to the Atiyah-Bott-Berline-Vergne localization formula for an equivariant form on the symplectic cut of M with respect to a certain cone, and then, if necessary, iterate this process using other cones. When all cones used to produce the formula are one-dimensional we recover, as a special case, the localization formula of Guillemin and Kalkman. Using similar ideas, for a special choice of the cone (whose dimension is equal to that of T) we give a new proof of the Jeffrey-Kirwan localization formula. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0310222 | |
| dc.identifier | http://arxiv.org/abs/math/0310222 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68861 | |
| dc.subject | Symplectic Geometry | |
| dc.title | Localization theorems by symplectic cuts | |
| dc.type | text |