Abstract commensurators of braid groups, with
Let B_n be the braid group on n > 3 strands and Mod(S) 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.
We also show that Tv is itself isomorphic to a semidirect product
of an infinite dimensional rational vector space with the multiplicative
group of non-zero rational numbers.