Geodesic
Combinatorial Miller–Morita–Mumford classes and Witten cycles
Igusa, Kiyoshi1
1Department of Mathematics, Brandeis University, Waltham MA 02454-9110, USA
Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 473-520
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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.

DOI : 10.2140/agt.2004.4.473
Keywords: mapping class group, fat graphs, ribbon graphs, tautological classes, Miller–Morita–Mumford classes, Witten conjecture, Stasheff associahedra

Igusa, Kiyoshi  1

1 Department of Mathematics, Brandeis University, Waltham MA 02454-9110, USA 
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Igusa, Kiyoshi. Combinatorial Miller–Morita–Mumford classes and Witten cycles. Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 473-520. doi: 10.2140/agt.2004.4.473

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