Braid groups and discrete diffeomorphisms of the punctured disk

2015/11/30 by Sam Nariman, Nariman, Sam
Mathematics · #55R10 #57R32 #57R50 #58D05 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1511.09369

openalex publication_date 2015/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Br_2g+2\hookrightarrow Mod_g,2 to a group homomorphism between diffeomorphism groups.

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