Cohomology of moduli spaces

2003/05/24 by Frances Kirwan
Mathematics · #math.AG #msc:14H10 #msc:14H15 #msc:32G15 #msc:55R40 #msc:57R20

paper · pdf

published as ICM 2002, Vol 1, 363-382 · ICM talk; 18 pages

arxiv created 2003/05/24 · arxiv updated 2009/11/30

Abstract

Some recent progress towards understanding the cohomology of moduli spaces of curves is described. Madsen and Weiss have given a proof of a generalisation of Mumford's conjecture on the stable cohomology of these moduli spaces M_g, and other contributors have made advances related to Faber's conjectures on the tautological ring of M_g.

Related

• Divisors in the moduli spaces of curves
• Tautological and non-tautological cohomology of the moduli space of curves
• Stability phenomena in the topology of moduli spaces
• The moduli space of curves and its invariants
• Strings and the stable cohomology of mapping class groups