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Fixed subgroups in Artin groups
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AI
DOI：10.4171/ggd/920.png)
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Abstract
En 中文
We study fixed subgroups of automorphisms of any large-type Artin group A(Gamma). We define a natural subgroup Aut Gamma (A(Gamma)) of Aut(A(Gamma)), and for every gamma is an element of Aut Gamma (A(Gamma)), we find the isomorphism type of Fix(gamma) and a generating set for a finite index subgroup. We show that Fix(gamma) is a finitely generated Artin group, with a uniform bound on the rank in terms of the number of vertices of P. Finally, we provide a natural geometric characterisation of the subgroup Autr (A(Gamma)), which informally is the maximal subgroup of Aut(A(Gamma)) leaving the Deligne complex of A(Gamma) invariant.
Keywords:
Artin groups
automorphisms
fixed subgroups
Artin groups
automorphisms
fixed subgroups
Journal
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50
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