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2020 Monopole contributions to refined Vafa–Witten invariants
Ties Laarakker
Geom. Topol. 24(6): 2781-2828 (2020). DOI: 10.2140/gt.2020.24.2781

Abstract

We study the monopole contribution to the refined Vafa–Witten invariant recently defined by Maulik and Thomas (work in progress). We apply the results of Gholampour and Thomas (to appear in Compos. Math.) to prove a universality result for the generating series of contributions of Higgs pairs with 1–dimensional weight spaces. For prime rank, these account for the entire monopole contribution by a theorem of Thomas. We use toric computations to determine part of the generating series and find agreement with the conjectures of Göttsche and Kool (Pure Appl. Math. Q. 14 (2018) 467–513) for ranks 2 and 3.

Citation

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Ties Laarakker. "Monopole contributions to refined Vafa–Witten invariants." Geom. Topol. 24 (6) 2781 - 2828, 2020. https://doi.org/10.2140/gt.2020.24.2781

Information

Received: 10 February 2019; Revised: 8 July 2019; Accepted: 9 December 2019; Published: 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194304
Digital Object Identifier: 10.2140/gt.2020.24.2781

Subjects:
Primary: 14C05, 14D20, 14J80

Rights: Copyright © 2020 Mathematical Sciences Publishers

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