Combinatorial Miller-Morita-Mumford classes and Witten cycles

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.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-23.abs.html

References in corpus (3)

• Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves
• Combinatorial classes on the moduli space of curves are tautological
• Increasing trees and Kontsevich cycles

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