The rational cohomology of the mapping class group vanishes in its virtual cohomological dimension (with T. Church and B. Farb) - [pdf] [ps]
Int. Math. Res. Not. (2012), no. 21, 5025–5030.

Abstract :
Let $\Mod_g$ be the mapping class group of a genus $g\geq 2$ surface. The group $\Mod_g$ has virtual cohomological dimension $4g-5$. In this note we use a theorem of Broaddus and the combinatorics of chord diagrams to prove that $H^{4g-5}(\Mod_g;\Q)=0$.