Mathematical Research Letters

Volume 23 (2016)

Number 5

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

Pages: 1351 – 1367



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


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.


equivariant index, quantization conjecture

2010 Mathematics Subject Classification

Primary 53D50. Secondary 19K56, 58J20.

Accepted 23 March 2015

Published 12 January 2017