Intersection numbers with Witten's top Chern class

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 [15], to find an algorithm for computing the intersection numbers of the Witten class with powers of the ψ-classes (or tautological classes) over any moduli space of r-spin structures, in short, all numbers involved in Witten's conjecture.

27 pages

References in corpus (3)

• An algebro-geometric proof of Witten's conjecture
• A simple proof of Witten conjecture through localization
• Witten's top Chern class via K-theory

Cited by in corpus (7)

• Tautological relations and the r-spin Witten conjecture
• Integrals of psi-classes over double ramification cycles
• The Witten equation, mirror symmetry and quantum singularity theory
• Equivalence of ELSV and Bouchard-Mariño conjectures for $r$-spin Hurwitz numbers
• A new proof of Faber's intersection number conjecture
• Formal pseudodifferential operators and Witten's r-spin numbers
• Buryak-Okounkov formula for the $n$-point function and a new proof of the Witten conjecture