Symplectic Surgery and the Spin-C Dirac operator
| dc.creator | Meinrenken, Eckhard | |
| dc.date | 1995-04-26 | |
| dc.date | 1996-12-30 | |
| dc.date.accessioned | 2026-07-07T08:59:07Z | |
| dc.date.available | 2026-07-07T08:59:07Z | |
| dc.description | Let $G$ be a compact connected Lie group, and $M$ a compact Hamiltonian $G$-space, with moment map $J$. For each $G$-equivariant Hermitian vector bundle $E$ over $M$, one has an associated twisted Spin-C Dirac operator, whose equivariant index is a symplectic invariant of $E$. In the present paper, we study gluing properties of the equivariant index under "symplectic cutting" operations. Our main application is a proof of the Guillemin-Sternberg conjecture, which says that if $E=L$ is a quantizing line bundle and $0$ a regular value of $J$, the multiplicity of the trivial representation in the equivariant index is equal to the Riemann-Roch number of the symplectic quotient. This generalizes previous results for the case that $G=T$ is abelian. | |
| dc.description | 30 pages, AMS-LaTeX. To appear in Advances in Mathematics. Revised version: Minor errors corrected, proofs simplified | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9504002 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9504002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147593 | |
| dc.subject | Differential Geometry | |
| dc.title | Symplectic Surgery and the Spin-C Dirac operator | |
| dc.type | text |