Arkiv för Matematik

Volume 57 (2019)

Number 1

Cohomological field theories with non-tautological classes

Pages: 191 – 213



R. Pandharipande (Departement Mathematik, Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland)

D. Zvonkine (Laboratoire Mathématique de Versailles, CNRS and Versailles St-Quentin University, Versailles, France)


A method of constructing Cohomological Field Theories (CohFTs) with unit using minimal classes on the moduli spaces of curves is developed. As a simple consequence, CohFTs with unit are found which take values outside of the tautological cohomology of the moduli spaces of curves. A study of minimal classes in low genus is presented in the Appendix by D. Petersen.

Appendix by D. Peterson (Matematiska institutionen, Stockholms universitet, Stockholm, Sweden. E-mail:

A correction was made to this article’s author credits on 2019 June 13.

Received 11 March 2018

Received revised 22 April 2018

Accepted 28 May 2018

Published 3 May 2019