Braid groups, mapping class groups and their homology with twisted coefficients
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We consider the Birman-Hilden inclusion φ:Br2g+1→Γg,1 of the braid group into the mapping class group of an orientable surface with boundary, and prove that φ is stably trivial in homology with twisted coefficients in the symplectic representation H1(Σg,1) of the mapping class group; this generalises a result of Song and Tillmann regarding homology with constant coefficients. Furthermore we show that the stable homology of the braid group with coefficients in φ∗(H1(Σg,1)) has only 4-torsion.
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - 2022|