The rational cohomology of the mapping class group vanishes in its   virtual cohomological dimension
  Let Mod_g be the mapping class group of a genus g >= 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. 
Thomas Church, Benson Farb, and Andrew Putman
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