Trees, homology, and automorphism groups of right-angled Artin groups
نویسندگان
چکیده
منابع مشابه
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.
متن کاملAnti-trees and right-angled Artin subgroups of braid groups
We prove that an arbitrary right-angled Artin group G admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree. Consequently, G admits quasi-isometric group embeddings into a pure braid group and into the area-preserving diffeomorphism groups of the 2–disk and the 2–sphere, answering questions due to Crisp–Wiest and M. Kapovich. Another co...
متن کاملPeak reduction and finite presentations for automorphism groups of right-angled Artin groups
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...
متن کاملOn Solvable Subgroups of Automorphism Groups of Right-Angled Artin Groups
For any right-angled Artin group, we show that its outer automorphism group contains either a finite-index nilpotent subgroup or a nonabelian free subgroup. This is a weak Tits alternative theorem. We find a criterion on the defining graph that determines which case holds. We also consider some examples of solvable subgroups, including one that is not virtually nilpotent and is embedded in a no...
متن کاملRight-angled Artin Groups and Their Subgroups
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2018
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-018-0854-y