The $S_n$-equivariant top weight Euler characteristic of $M_{g,n}$

Abstract

We prove a formula, conjectured by Zagier, for the $S_n$-equivariant Euler characteristic of the top weight cohomology of $M_{g,n}$.Comment: 26 pages, 5 figures; v2: added references to related work of Tsopm\'en\'e and Turchin and of Willwacher and \v{Z}ivkovi\'c, along with Remark 1.8, which explains the connection