Combinatorial Miller-Morita-Mumford classes and Witten cycles

Kiyoshi Igusa

备注：: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-23.abs.html
发表信息：: Algebr. Geom. Topol. 4 (2004) 473-520
DOI：: 10.2140/agt.2004.4.473

英文摘要：

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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