Mathematical Research Letters
Volume 23 (2016)
$S^1$-equivariant local index and transverse index for non-compact symplectic manifolds
Pages: 1351 – 1367
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