Combinatorial Miller-Morita-Mumford classes and Witten cycles
Geometric Topology
2014-10-01 v2 High Energy Physics - Theory
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.
Cite
@article{arxiv.math/0207042,
title = {Combinatorial Miller-Morita-Mumford classes and Witten cycles},
author = {Kiyoshi Igusa},
journal= {arXiv preprint arXiv:math/0207042},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-23.abs.html