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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
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
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