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


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.)


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.


quantum cohomology, GIT quotients

2010 Mathematics Subject Classification

14L24, 14N35, 53D45

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