Graph cohomology and Kontsevich cycles

TL;DR

This paper explores the relationship between graph cohomology, Kontsevich cycles, and Miller-Morita-Mumford classes, providing methods to compute polynomial coefficients using Stasheff polyhedra and previous results.

Contribution

It introduces a novel approach to compute coefficients of polynomials in the cohomology of mapping class groups via graph homology and polyhedral techniques.

Findings

Coefficients of Kontsevich cycles can be computed using Stasheff polyhedra.

Establishes a connection between graph cohomology and Miller-Morita-Mumford classes.

Provides explicit computational methods for these polynomial coefficients.

Abstract

The dual Kontsevich cycles in the double dual of associative graph homology correspond to polynomials in the Miller-Morita-Mumford classes in the integral cohomology of mapping class groups. I explain how the coefficients of these polynomials can be computed using Stasheff polyhedra and results from my previous paper GT/0207042.