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

TL;DR

This paper constructs new non-trivial cohomology classes on strata of differentials in moduli spaces, advancing understanding of their geometric and topological properties.

Contribution

It introduces methods to produce non-tautological cohomology classes using boundary stratification of multi-scale differentials.

Findings

Construction of non-trivial cohomology classes

Identification of non-tautological classes in moduli spaces

Application of boundary stratification techniques

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.