Combinatorial Miller-Morita-Mumford classes and Witten cycles

Details Combinatorial Miller-Morita-Mumford classes and Witten cycles Combinatorial Miller-Morita-Mumford classes and Witten cycles

2002-07-04

arxiv.org/abs/math/0207042v2

Algebr. Geom. Topol. 4 (2004) 473-520

Mathematics

Geometric Topology

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

Scientific paper

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.

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