منابع مشابه
Linearity of Artin Groups of Finite Type
Recent results on the linearity of braid groups are extended in two ways. We generalize the Lawrence Krammer representation as well as Krammer’s faithfulness proof for this linear representation to Artin groups of finite type.
متن کاملAutomorphism 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...
متن کاملAn Isoperimetric Inequality for Artin Groups of Finite Type
We show that Artin groups of finite type satisfy a quadratic isoperimetric inequality. Moreover we describe an explicit algorithm to solve the word problem in quadratic time.
متن کاملArtin groups of euclidean type
Coxeter groups were introduced by Jacques Tits in the 1960s as a natural generalization of the groups generated by reflections which act geometrically (which means properly discontinuously cocompactly by isometries) on spheres and euclidean spaces. And ever since their introduction their basic structure has been reasonably well understood [BB05, Bou02, Dav08]. More precisely, every Coxeter grou...
متن کاملCovers of D-Type Artin Groups
We study certain quotients of generalized Artin groups which have a natural map onto D-type Artin groups, where the generalized Artin group A(T ) is defined by a signed graph T . Then we find a certain quotient G(T ) according to the graph T , which also have a natural map onto A(Dn). We prove that G(T ) is isomorphic to a semidirect product of a group K(m,n), with the Artin group A(Dn), where ...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2002
ISSN: 0021-2172,1565-8511
DOI: 10.1007/bf02785852