Automorphism groups of some affine and finite type Artin groups
نویسندگان
چکیده
منابع مشابه
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...
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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.
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We generalize the peak reduction algorithm (Whitehead’s theorem) for free groups to a theorem about a general right-angled Artin group A . As an application, we find a finite presentation for the automorphism group AutA that generalizes McCool’s presentation for the automorphism group of a finite rank free group. We also consider a stronger generalization of peak reduction, giving a counterex...
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The result of this paper is the determination of the cohomology of Artin groups of type An, Bn and Ãn with non-trivial local coefficients. The main result is an explicit computation of the cohomology of the Artin group of type Bn with coefficients over the module Q[q±1, t±1]. Here the first n− 1 standard generators of the group act by (−q)-multiplication, while the last one acts by (−t)-multipl...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2005
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2005.v12.n3.a4