ABSTRACT: The Miller-Morita-Mumford classes are cohomology classes for the mapping class group of oriented surfaces. They are given by rational cocycles on the category of fat graphs (=ribbon graphs) which are expectation values of cyclic permutations. These cocycles will only be nonzero on the Stasheff associahedra which are dual to the Witten cycles W_2k. This proves the Witten conjecture that the MMM classes are dual to these Witten cycles. Cup products of the cyclic cocycles are only nonzero on the products of associahedra dual to the Kontsevich cycles. This proves one of Kontsevich's conjectures as refined by Arbarello and Cornalba.

For further information visit the Seminar web site at http://www.northeastern.edu/martsinkovsky/p/rtrt.html  or contact Alex Martsinkovsky <alexmart@neu.edu>