Abstract commensurators of braid groups

Details Abstract commensurators of braid groups Abstract commensurators of braid groups

2005-01-26

arxiv.org/abs/math/0501480v1

Mathematics

Group Theory

10 pages

Scientific paper

Let B_n be the braid group on n strands, with n at least 4, and let Mod(S) be the extended mapping class group of the sphere with n+1 punctures. We show that the abstract commensurator of B_n is isomorphic to a semidirect product of Mod(S) with a group we refer to as the transvection subgroup, Tv(B_n). We also show that Tv(B_n) is itself isomorphic to a semidirect product of an infinite dimensional rational vector space with the multiplicative group of nonzero rational numbers.

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