Discoveries / geometry-topology

Kontsevich's Asphericity Conjecture for Strata of Differentials

A conjecture attributed to Kontsevich holds that strata of quadratic differentials are aspherical, that is orbifold $K(\pi,1)$ spaces. False: when there are at least four zeros or poles, no connected component of a genus-one stratum is an orbifold $K(\pi,1)$, giving infinitely many counterexamples, along with counterexamples for associated stability spaces.