Geometry & Topology 8 (2004) 969–1012

DOI: 10.2140/gt.2004.8.969

arXiv: math.AT/0303353

Abstract

It is known that the combinatorial classes in the cohomology of the mapping class group of punctures surfaces defined by Witten and Kontsevich are polynomials in the adjusted Miller–Morita–Mumford classes. The first two coefficients were computed by the first author in earlier papers. The present paper gives a recursive formula for all of the coefficients. The main combinatorial tool is a generating function for a new statistic on the set of increasing trees on 2n+1 vertices. As we already explained this verifies all of the formulas conjectured by Arbarello and Cornalba. Mondello has obtained similar results using different methods.

Keywords

ribbon graphs, graph cohomology, mapping class group, Sterling numbers, hypergeometric series, Miller–Morita–Mumford classes, tautological classes

Mathematical Subject Classification

Primary: 55R40

Secondary: 05C05

References

Forward citations

Publication

Received: 30 March 2003
Accepted: 11 June 2004
Published: 8 July 2004
Proposed: Shigeyuki Morita
Seconded: Ralph Cohen, Martin Bridson

Authors