Abstract
Abstract We show that each of the Artin groups of type Bn and Dn can be presented as a semidirect product F ⋊ ℬ n , where F is a free group and ℬ n is the n-string braid group. We explain how these semidirect product structures arise quite naturally from fibrations, and observe that, in each case, the action of the braid group ℬ n on the free group F is classical. We prove that, for each of the semidirect products, the group of automorphisms which leave invariant the normal subgroup F is small: namely, Out(A(Bn ), F ) has order 2, and Out(A(Dn ), F ) has order 4 if n is even and 2 if n is odd. It is known that the Artin group of type Dn may be viewed as an index 2 subgroup of the n-string braid group over a disk with a degree 2 orbifold point. We show that this orbifold braid group has outer automorphism group of order 2, for all n ≥ 2.
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