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arXiv · 1511.09369

Braid groups and discrete diffeomorphisms of the punctured disk

Sam Nariman
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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.

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Sam Nariman. 2015-11-30. Braid groups and discrete diffeomorphisms of the punctured disk. https://arxiv.org/abs/1511.09369

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