The equivariant local index of the reduced space in the symplectic cutting

TL;DR

This paper calculates the equivariant local index for reduced spaces obtained via symplectic cutting, assuming the reduced space is compact, contributing to the understanding of symplectic geometry and index theory.

Contribution

It introduces a method to compute the equivariant local index in symplectic cut spaces with compact reduced spaces, advancing the theoretical framework.

Findings

Explicit formula for the equivariant local index

Application to symplectic geometry problems

Extension of index theory in symplectic cuts

Abstract

We compute the equivariant local index for the reduced space in a symplectic cut space, provided that the reduced space is compact.