2010
DOI: 10.4171/ggd/84
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On right-angled Artin groups without surface subgroups

Abstract: Abstract. We study the class N of graphs, the right-angled Artin groups defined on which do not contain closed hyperbolic surface subgroups. We prove that a presumably smaller class N 0 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 0 . Mathematics Subject Classification (2010). Primary 20F36, 20F65; Secondary 05C25.

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Cited by 10 publications
(3 citation statements)
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“…Many right-angled Artin groups contain quasi-isometrically embedded surface subgroups; see [40,11] (though the question of exactly which right-angled Artin groups contain surface subgroups is still open; see for example [16,23,24,10,39]). There are also constructions of surface subgroups of the mapping class group [1,26,15].…”
Section: Remarksmentioning
confidence: 99%
“…Many right-angled Artin groups contain quasi-isometrically embedded surface subgroups; see [40,11] (though the question of exactly which right-angled Artin groups contain surface subgroups is still open; see for example [16,23,24,10,39]). There are also constructions of surface subgroups of the mapping class group [1,26,15].…”
Section: Remarksmentioning
confidence: 99%
“…Further sufficient conditions were found by Gordon and the author [14] and Kim and the author [23]. Kim and Oum answered Question 1 when is the double of a rank-two free group [22].…”
Section: Question 1 Does Every One-ended Hyperbolic Group Have a Surfmentioning
confidence: 88%
“…Sometimes called Baumslag's Lemma, this result plays a fundamental role in the theory of limit groups; see [105] and references therein. Baumslag's Lemma generalizes for multiple "twisting words" [69,5], and also for torsion-free wordhyperbolic groups [55]. We will present a continuous version of Baumslag's lemma in this section that will imply both of these generalizations.…”
Section: Lemma 31 ([6]mentioning
confidence: 97%