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

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.

12 pages. The title changed. Final version. Some explanations added. Typos corrected. References uploaded. : Journal reference added

References in corpus (1)

• Applications of Equivariant Cohomology

Cited by in corpus (1)

• A Danilov-type formula for toric origami manifolds via localization of index