Algebraic and Geometric Topology 4 (2004),
paper no. 23, pages 473-520.
Combinatorial Miller-Morita-Mumford classes and Witten cycles
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.
Mapping class group, fat graphs, ribbon graphs, Miller-Morita-Mumford
classes, tautological classes, Witten conjecture, Stasheff associahedra
AMS subject classification.
Secondary: 55R40, 57M15.
Submitted: 18 December 2003.
(Revised: 26 May 2004.)
Accepted: 6 July 2004.
Published: 8 July 2004.
Notes on file formats
Department of Mathematics, Brandeis University
Waltham, MA 02454-9110, USA
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