Open Access
Translator Disclaimer
2016 Spin Hurwitz numbers and topological quantum field theory
Sam Gunningham
Geom. Topol. 20(4): 1859-1907 (2016). DOI: 10.2140/gt.2016.20.1859


Spin Hurwitz numbers count ramified covers of a spin surface, weighted by the size of their automorphism group (like ordinary Hurwitz numbers), but signed ± 1 according to the parity of the covering surface. These numbers were first defined by Eskin, Okounkov and Pandharipande in order to study the moduli of holomorphic differentials on a Riemann surface. They have also been related to Gromov–Witten invariants of complex 2–folds by work of Lee and Parker and work of Maulik and Pandharipande. In this paper, we construct a (spin) TQFT which computes these numbers, and deduce a formula for any genus in terms of the combinatorics of the Sergeev algebra, generalizing the formula of Eskin, Okounkov and Pandharipande. During the construction, we describe a procedure for averaging any TQFT over finite covering spaces based on the finite path integrals of Freed, Hopkins, Lurie and Teleman.


Download Citation

Sam Gunningham. "Spin Hurwitz numbers and topological quantum field theory." Geom. Topol. 20 (4) 1859 - 1907, 2016.


Received: 8 February 2014; Revised: 11 August 2015; Accepted: 24 September 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1347.81070
MathSciNet: MR3548460
Digital Object Identifier: 10.2140/gt.2016.20.1859

Primary: 81T45

Keywords: spin Hurwitz numbers , topological quantum field theory

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.20 • No. 4 • 2016
Back to Top