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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.


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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
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