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2008 Intersection numbers with Witten's top Chern class
Sergey Shadrin, Dimitri Zvonkine
Geom. Topol. 12(2): 713-745 (2008). DOI: 10.2140/gt.2008.12.713


Witten’s top Chern class is a particular cohomology class on the moduli space of Riemann surfaces endowed with r–spin structures. It plays a key role in Witten’s conjecture relating to the intersection theory on these moduli spaces.

Our first goal is to compute the integral of Witten’s class over the so-called double ramification cycles in genus 1. We obtain a simple closed formula for these integrals.

This allows us, using the methods of the first author [Int. Math. Res. Not. 38 (2003) 2051-2094], to find an algorithm for computing the intersection numbers of the Witten class with powers of the ψ–classes over any moduli space of r–spin structures, in short, all numbers involved in Witten’s conjecture.


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Sergey Shadrin. Dimitri Zvonkine. "Intersection numbers with Witten's top Chern class." Geom. Topol. 12 (2) 713 - 745, 2008.


Received: 5 January 2006; Revised: 22 January 2008; Accepted: 5 October 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1141.14012
MathSciNet: MR2403799
Digital Object Identifier: 10.2140/gt.2008.12.713

Primary: 14H10
Secondary: 14H70

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.12 • No. 2 • 2008
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