Norm-square localization for Hamiltonian $LG$-spaces

TL;DR

This paper develops a formula for twisted Duistermaat-Heckman distributions in Hamiltonian LG-spaces, localizing computations at critical points of the norm-square of the moment map using quasi-Hamiltonian spaces and Hamiltonian cobordism.

Contribution

It introduces a new localization formula for twisted Duistermaat-Heckman distributions in the context of Hamiltonian LG-spaces, utilizing Hamiltonian cobordism techniques.

Findings

Localization at critical points simplifies computations.

The formula can be computed in cross-sections.

Utilizes quasi-Hamiltonian G-spaces and cobordism methods.

Abstract

We prove a formula for twisted Duistermaat-Heckman distributions associated to a Hamiltonian $LG$-space. The terms of the formula are localized at the critical points of the norm-square of the moment map, and can be computed in cross-sections. Our main tools are the theory of quasi-Hamiltonian $G$-spaces, as well as the Hamiltonian cobordism approach to norm-square localization introduced recently by Harada and Karshon.