Increasing trees and Kontsevich cycles

Details Increasing trees and Kontsevich cycles Increasing trees and Kontsevich cycles

2003-03-27

arxiv.org/abs/math/0303353v2

Geom. Topol. 8(2004) 969-1012

Mathematics

Algebraic Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper26.abs.html

Scientific paper

It is known that the combinatorial classes in the cohomology of the mapping class group of punctures surfaces defined by Witten and Kontsevich are polynomials in the adjusted Miller-Morita-Mumford classes. The leading coefficient was computed in [Kiyoshi Igusa: Algebr. Geom. Topol. 4 (2004) 473-520]. The next coefficient was computed in [Kiyoshi Igusa: math.AT/0303157, to appear in Topology]. The present paper gives a recursive formula for all of the coefficients. The main combinatorial tool is a generating function for a new statistic on the set of increasing trees on 2n+1 vertices. As we already explained in the last paper cited this verifies all of the formulas conjectured by Arbarello and Cornalba [J. Alg. Geom. 5 (1996) 705--749]. Mondello [math.AT/0303207, to appear in IMRN] has obtained similar results using different methods.

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