Non-trivial and Non-tautological Cohomology of Strata of Differentials

Abstract

In this paper we construct various non-trivial and non-tautological cohomology classes on compactified and uncompactified strata of curves with a differential, by using the geometry of the boundary stratification of the moduli space of multi-scale differentials.

With an appendix written jointly with Dawei Chen and Martin Möller