The rational cohomology of the mapping class group vanishes in its virtual cohomological dimension

Published 2 Aug 2011 in math.GT, math.AT, and math.GR | (1108.0622v3)

Abstract: 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.

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