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Intersection numbers with
Witten's top Chern class
Sergey Shadrin and Dimitri Zvonkine |
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Geometry & Topology 12 (2008) 713–745
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Abstract |
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Witten’s top Chern class is a particular cohomology class on the moduli space of Riemann surfaces endowed with –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 –classes over any moduli space of –spin structures, in short, all numbers involved in Witten’s conjecture. |
Keywords
moduli space of curves, intersection theory, Witten top
Chern class
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Mathematical Subject Classification 2000
Primary: 14H10
Secondary: 14H70
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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
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Authors |
| Sergey Shadrin | |
| Korteweg–de Vries Institute for
Mathematics Plantage Muidergracht 24 1018 TV Amsterdam The Netherlands and Institute of System Research Nakhimovskii Prospekt 36-1 117218 Moscow Russia |
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| Dimitri Zvonkine | |
| Poncelet Laboratory, CNRS and Independent University of Moscow Bolshoi Vlassievsky per, 11 119002 Moscow Russia |
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