Tautological and non-tautological cohomology of the moduli space of curves

By R. Pandharipande, Carel Faber. 2011

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After a short exposition of the basic properties of the tautological ring of Mg,n, we explain three methods of detecting non-tautological classes in cohomology. The first is via curve counting over finite fields. The second is by obtaining length bounds on the action of the symmetric group n on tautological classes. The third is via classical boundary geometry. Several new non-tautological classes are found.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5d9231da44b303c869413f3fce0900c5ab5b5385