Year: 2004
Type: article
Abstract: 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 [4].The next coefficient was computed in [6].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 [6] this verifies all of the formulas conjectured by Arbarello and Cornalba [1].Mondello [10] has obtained similar results using different methods.
Source: Geometry & Topology
Authors: Kiyoshi Igusa, Michael Kleber
Institution: Brandeis University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2141052237