John Crisp, Luis Paris
Artin groups of type B and D
We show that each of the Artin groups of type Bn and
Dn can be presented as a semidirect product F ? ?n,
where F is a free group and ?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 ?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.
Advances in Geometry, Walter de Gruyter
Print ISSN: 1615-715X
Volume: 5, 10/2005
Seiten: 607 - 636
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