Geometry and Topology 12 (2008) 713–745

DOI: 10.2140/gt.2008.12.713

Abstract

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.

Keywords

moduli space of curves, intersection theory, Witten top Chern class

Mathematical Subject Classification

Primary: 14H10

Secondary: 14H70

References

Publication

Received: 5 January 2006
Revised: 22 January 2008
Accepted: 5 October 2007
Published: 12 May 2008
Proposed: Eleny Ionel
Seconded: Jim Bryan, Yasha Eliashberg

Authors