%0 Journal Article
%T $S^1$-equivariant local index and transverse index for non-compact symplectic manifolds
%A Hajime Fujita
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1303.4485v4