Algebraic & Geometric Topology 4 (2004) 473–520

DOI: 10.2140/agt.2004.4.473

arXiv: math.GT/0207042

Abstract

We obtain a combinatorial formula for the Miller–Morita–Mumford classes for the mapping class group of punctured surfaces and prove Witten’s conjecture that they are proportional to the dual to the Witten cycles. The proportionality constant is shown to be exactly as conjectured by Arbarello and Cornalba [J. Alg. Geom. 5 (1996) 705–749]. We also verify their conjectured formula for the leading coefficient of the polynomial expressing the Kontsevich cycles in terms of the Miller–Morita–Mumford classes.

Keywords

mapping class group, fat graphs, ribbon graphs, tautological classes, Miller–Morita–Mumford classes, Witten conjecture, Stasheff associahedra

Mathematical Subject Classification

Primary: 57N05

Secondary: 55R40, 57M15

References

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Publication

Received: 18 December 2003
Revised: 26 May 2004
Accepted: 6 July 2004
Published: 8 July 2004

Authors