Pure and Applied Mathematics Quarterly

Volume 19 (2023)

Number 4

Special Issue in honor of Victor Guillemin

Guest Editors: Yael Karshon, Richard Melrose, Gunther Uhlmann, and Alejandro Uribe

Quantum Witten localization

Pages: 1943 – 1973

DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n4.a9

Authors

Eduardo González (Department of Mathematics, University of Massachusetts, Boston, Mass., U.S.A.)

Chris T. Woodward (Mathematics, Hill Center, Rutgers University, Piscataway, New Jersey, U.S.A.)

Abstract

We prove a quantum version of the localization formula of Witten $\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=1185834}{[31]}$, see also $[\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=1792291}{28}$, $\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=1722000}{22}$, $\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=2198772}{35}$], that relates invariants of a GIT quotient with the equivariant invariants of the action.

Keywords

quantum cohomology, GIT quotients

2010 Mathematics Subject Classification

14L24, 14N35, 53D45

Full Text (PDF format)

The authors were partially supported by grants DMS1104670 and DMS1207194.

A previous version of this article was titled “Area-dependence in gauged Gromov–Witten theory”.

Received 11 July 2021

Received revised 1 June 2022

Accepted 22 July 2022

Published 20 November 2023