Embedability between right-angled Artin groups
نویسندگان
چکیده
منابع مشابه
Embedability between right-angled Artin groups
In this article we study the right-angled Artin subgroups of a given right-angled Artin group. Starting with a graph Γ, we produce a new graph through a purely combinatorial procedure, and call it the extension graph Γ of Γ. We produce a second graph Γ k , the clique graph of Γ, by adding extra vertices for each complete subgraph of Γ. We prove that each finite induced subgraph Λ of Γ gives ris...
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We define a family of quasi-isometry invariants of groups called higher divergence functions, which measure isoperimetric properties “at infinity.” We give sharp upper and lower bounds on the divergence functions for right-angled Artin groups, using different pushing maps on the associated cube complexes. In the process, we define a class of RAAGs we call orthoplex groups, which have the proper...
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We consider the question of which right-angled Artin groups contain closed hyperbolic surface subgroups. It is known that a right-angled Artin group A(K) has such a subgroup if its defining graph K contains an n-hole (i.e. an induced cycle of length n) with n ≥ 5. We construct another eight “forbidden” graphs and show that every graph K on ≤ 8 vertices either contains one of our examples, or co...
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These are notes for a course offered at Yale University in the spring semester of 2013.
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In this paper we study topological invariants of a class of random groups. Namely, we study right angled Artin groups associated to random graphs and investigate their Betti numbers, cohomological dimension and topological complexity. The latter is a numerical homotopy invariant reflecting complexity of motion planning algorithms in robotics. We show that the topological complexity of a random ...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2013
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2013.17.493