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

Thomas Church; Benson Farb; Andrew Putman

doi:10.1093/imrn/rnr208

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arXiv · 1108.0622

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

Thomas Church·Benson Farb·Andrew Putman

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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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Thomas Church, Benson Farb, Andrew Putman. 2011-10-06. The rational cohomology of the mapping class group vanishes in its virtual cohomological dimension. https://doi.org/10.1093/imrn%2Frnr208

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