Journal of Symplectic Geometry

Volume 19 (2021)

Number 6

Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions

Pages: 1281 – 1337

DOI: https://dx.doi.org/10.4310/JSG.2021.v19.n6.a1

Authors

Benjamin Delarue (Institut für Mathematik, Universität Paderborn, Paderborn, Germany)

Pablo Ramacher (Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Germany)

Abstract

We derive a complete asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions on arbitrary symplectic manifolds, characterizing the coefficients in the expansion as integrals over the symplectic strata of the corresponding Marsden–Weinstein reduced space and distributions on the Lie algebra. The obtained coefficients involve singular contributions of the lower-dimensional strata related to numerical invariants of the fixed-point set.

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The first-named author was formerly known as Benjamin Küster.

Received 2 July 2020

Accepted 24 January 2021

Published 8 June 2022