Braid groups and discrete diffeomorphisms of the punctured disk

Abstract

We show that the group cohomology of the diffeomorphisms of the disk with $n$ punctures has the cohomology of the braid group of $n$ strands as the summand. As an application of this method, we also prove that there is no cohomological obstruction to lifting the "standard" embedding ${\mathrm{Br}}_{2g+2}\hookrightarrow {\mathrm{Mod}}_{g,2}$ to a group homomorphism between diffeomorphism groups.

Thoroughly revised. To appear in Mathematische Zeitschrift

References in corpus (4)

• Homological stability for moduli spaces of high dimensional manifolds. I
• Stable homology of surface diffeomorphism groups made discrete
• Homological stability and stable moduli of flat manifold bundles
• On the non-realizability of braid groups by diffeomorphisms

Cited by in corpus (2)

• Stable homology of surface diffeomorphism groups made discrete
• On the non-realizability of braid groups by diffeomorphisms