The cohomological dimension of the terms of the Johnson filtration

Abstract

We prove that the $k$th term of the Johnson filtration of a closed, orientable surface of genus $g\ge 2$ has cohomological dimension $2g-3$ for all $k\ge 3$ and $g\ge 2$. This answers a question of Farb and Bestvina--Bux--Margalit.

arXiv commentMajor revision, corrected an error in a proof in Section 2, submitted version