Homology of some Artin and twisted Artin Groups

Homology of some Artin and twisted Artin Groups

We begin the paper with a simple formula for the second integral homology of a range of Artin groups. The formula is derived from a polytopal classifying space. We then introduce the notion of a twisted Artin group and obtain polytopal classifying spaces for a range of such groups. We demonstrate that these explicitly constructed spaces can be implemented on a computer and used in homological c...

Garside structures for ( some more ) Artin groups

Automorphism Groups of Some Affine and Finite Type Artin Groups

We observe that, for fixed n ≥ 3, each of the Artin groups of finite type An, Bn = Cn, and affine type Ãn−1 and C̃n−1 is a central extension of a finite index subgroup of the mapping class group of the (n + 2)-punctured sphere. (The centre is trivial in the affine case and infinite cyclic in the finite type cases). Using results of Ivanov and Korkmaz on abstract commensurators of surface mapping...

Artin Groups and Coxeter Groups

where the words on each side of these relations are sequences of mij letters where ai and aj alternate in the sequence. The matrix of values mij is a Coxeter matrix M = (mij)i,j∈I on I. These groups generalize the braid groups established in 1925 by E. Artin in a natural way and therefore we suggest naming them Artin groups. If one adds the relations ai = 1 to the relations in the presentation ...

Homology of Subgroups of Right-angled Artin Groups

We describe the (co)homology of a certain family of normal subgroups of right-angled Artin groups that contain the commutator subgroup, as modules over the quotient group. We do so in terms of (skew) commutative algebra of squarefree monomial ideals.