@inbook{d98d7037f6d04a189500e781ff2be48d,
title = "Tautological and non-tautological cohomology of the moduli space of curves",
abstract = "After a short exposition of the basic properties of the tautological ring of the moduli space of genus g Deligne-Mumford stable curves with n markings, 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 S_n on tautological classes. The third is via classical boundary geometry. Several new non-tautological classes are found.",
keywords = "Moduli, tautological classes, cohomology",
author = "C. Faber and R. Pandharipande",
year = "2013",
language = "English",
isbn = "978-1571462572",
series = "Advanced Lectures in Mathematics",
publisher = "International Press",
number = "24",
pages = "293--330",
editor = "G. Farkas and I. Morrison",
booktitle = "Handbook of Moduli",
}