English

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.

Keywords

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

R2 v1 2026-07-22T16:46:29.495Z