2011/10/06 by Tara E. Brendle, Tara Brendle, Dan Margalit +2
Mathematics · #20F36 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #math.GT #msc:20F36
paper · pdf · doi:10.48550/arxiv.1110.1397
26 pages, 4 figures
arxiv created 2011/10/06 · openalex publication_date 2011/10/06 · arxiv updated 2011/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The hyperelliptic Torelli group is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface and that also commute with some fixed hyperelliptic involution. We prove a Birman exact sequence for hyperelliptic Torelli groups, and we show that this sequence splits. As a consequence, we show that the hyperelliptic Torelli group is generated by Dehn twists if and only if it is generated by reducible elements. We also give an application to the kernel of the Burau representation.