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A new cohomology class on the moduli space of curves

Paul Norbury

Geometry & Topology 27 (2023) 2695–2761
Abstract

We define a collection Θg,n H4g4+2n(¯g,n, ) for 2g 2 + n > 0 of cohomology classes that restrict naturally to boundary divisors. We prove that the intersection numbers ¯ g,nΘg,n i=1nψimi can be recursively calculated. We conjecture that a generating function for these intersection numbers is a tau function of the KdV hierarchy. This is analogous to the conjecture of Witten proven by Kontsevich that a generating function for the intersection numbers ¯ g,n i=1nψimi is a tau function of the KdV hierarchy.

Keywords
moduli space, cohomology, spin structure
Mathematical Subject Classification
Primary: 14D23, 32G15, 53D45
References
Publication
Received: 2 April 2020
Revised: 22 September 2021
Accepted: 16 October 2021
Published: 19 September 2023
Proposed: Haynes R Miller
Seconded: Jim Bryan, Mark Gross
Authors
Paul Norbury
School of Mathematics and Statistics
University of Melbourne
Melbourne VIC
Australia

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