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

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

2011-08-02

arxiv.org/abs/1108.0622v3

Mathematics

Geometric Topology

4 pages. Final version, to appear in IMRN

Scientific paper

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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