Combinatorial classes on the moduli space of curves are tautological

Abstract

The combinatorial description via ribbon graphs of the moduli space of Riemann surfaces makes it possible to define combinatorial cycles in a natural way. Witten and Kontsevich first conjectured that these classes are polynomials in the tautological classes. We answer affirmatively to this conjecture and find recursively all the polynomials.

LaTeX2e, 57 pages, 16 figures (XYpic and PSTeX), to appear on IMRN

References in corpus (3)

• On a theorem of Kontsevich
• Combinatorial Miller-Morita-Mumford classes and Witten cycles
• Graph cohomology and Kontsevich cycles

Cited by in corpus (2)

• Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy
• Combinatorial Miller-Morita-Mumford classes and Witten cycles