Mathematical Research Letters

Volume 23 (2016)

Number 5

$S^1$-equivariant local index and transverse index for non-compact symplectic manifolds

Pages: 1351 – 1367

DOI: https://dx.doi.org/10.4310/MRL.2016.v23.n5.a5

Author

Hajime Fujita (Department of Mathematical and Physical Sciences, Japan Women’s University, Bunkyo-ku, Tokyo, Japan)

Abstract

We define an $S^1$-equivariant index for non-compact symplectic manifolds with Hamiltonian $S^1$-action. We use the perturbation by Dirac-type operator along the $S^1$-orbits. We give a formulation and a proof of quantization conjecture for this $S^1$-equivariant index. We also give comments on the relation between our $S^1$-equivariant index and the index of transverse elliptic operators.

Keywords

equivariant index, quantization conjecture

2010 Mathematics Subject Classification

Primary 53D50. Secondary 19K56, 58J20.

Accepted 23 March 2015

Published 12 January 2017