SURFACE SUBGROUPS OF RIGHT-ANGLED ARTIN GROUPS
نویسندگان
چکیده
منابع مشابه
Surface Subgroups of Right-Angled Artin Groups
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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We study the class N of graphs, the right-angled Artin groups defined on which do not contain surface subgroups. We prove that a presumably smaller class N ′ is closed under amalgamating along complete subgraphs, and also under adding bisimplicial edges. It follows that chordal graphs and chordal bipartite graphs belong to N ′.
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These are notes for a course offered at Yale University in the spring semester of 2013.
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Let G be the right-angled Artin group associated to the flag complex Σ and let π : G → Z be its canonical height function. We investigate the presentation theory of the groups Γn = π(nZ) and construct an algorithm that, given n and Σ, outputs a presentation of optimal deficiency on a minimal generating set, provided Σ is triangle-free; the deficiency tends to infinity as n → ∞ if and only if th...
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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...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2008
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196708004536