Artin groups of type B and D
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Abstract
We show that each of the Artin groups of type Bn and Dn can be presented as a semidirect product F ⋊ ℬn, where F is a free group and ℬn 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 ℬn 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.
Walter de Gruyter GmbH & Co. KG
Articles in the same Issue
- On antipodes on a convex polyhedron
- Extensions of isomorphisms for affine dual polar spaces and strong parapolar spaces
- Affine parts of topological unitals
- Flocks of topological circle planes
- Positivity, sums of squares and the multi-dimensional moment problem II
- Artin groups of type B and D
- Intersection of ACM-curves in ℙ3
- Die harmonischen Involutionen einer Möbiusebene
Articles in the same Issue
- On antipodes on a convex polyhedron
- Extensions of isomorphisms for affine dual polar spaces and strong parapolar spaces
- Affine parts of topological unitals
- Flocks of topological circle planes
- Positivity, sums of squares and the multi-dimensional moment problem II
- Artin groups of type B and D
- Intersection of ACM-curves in ℙ3
- Die harmonischen Involutionen einer Möbiusebene
