2020
DOI: 10.48550/arxiv.2007.16169
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Acylindrical hyperbolicity for Artin groups of dimension 2

Abstract: In this paper, we show that every irreducible 2-dimensional Artin group AΓ of rank at least 3 is acylindrically hyperbolic. We do this by applying a criterion of Martin to the action of AΓ on its modified Deligne complex. Along the way, we prove results of independent interests on the geometry of links of this complex.

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Cited by 2 publications
(3 citation statements)
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References 16 publications
(24 reference statements)
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“…Indeed, several complexes have been associated to Artin groups using the combinatorics of parabolic subgroups. For instance, Deligne complexes and their variants are built out of (cosets of) standard parabolic subgroups of spherical type (Charney & Davis, 1995), and have been used to study various aspects of Artin groups: K(π, 1)-conjecture (Charney & Davis, 1995, Paris, 2014, acylindrical hyperbolicity (Charney & Morris-Wright, 2019, Martin & Przytycki, 2019, Vaskou, 2020, Tits alternative (Martin & Przytycki, 2020), etc. More recently, using the connections between braid groups and mapping class groups, the irreducible parabolic subgroups have been used to define a possible analogue of the complex of curves for Artin groups of spherical type (Cumplido et al, 2019, Morris-Wright, 2021.…”
Section: Introductionmentioning
confidence: 99%
“…Indeed, several complexes have been associated to Artin groups using the combinatorics of parabolic subgroups. For instance, Deligne complexes and their variants are built out of (cosets of) standard parabolic subgroups of spherical type (Charney & Davis, 1995), and have been used to study various aspects of Artin groups: K(π, 1)-conjecture (Charney & Davis, 1995, Paris, 2014, acylindrical hyperbolicity (Charney & Morris-Wright, 2019, Martin & Przytycki, 2019, Vaskou, 2020, Tits alternative (Martin & Przytycki, 2020), etc. More recently, using the connections between braid groups and mapping class groups, the irreducible parabolic subgroups have been used to define a possible analogue of the complex of curves for Artin groups of spherical type (Cumplido et al, 2019, Morris-Wright, 2021.…”
Section: Introductionmentioning
confidence: 99%
“…The action of A ab on Lk D pv ab q has been studied by Vaskou in [Vas20]. In particular, the following result, which is a geometric counterpart of Lemma 2.6 will be useful in Section 5: Lemma 2.34 ([Vas20, Proposition 4.7]).…”
Section: 4mentioning
confidence: 99%
“…This question has been answered positively for most standard classes of Artin groups, such as right-angled Artin groups [CS11], Artin groups of finite type [CW:], Artin groups of Euclidean type [Cal20], Artin groups whose underlying presentation graph is not a join [RMW19], and two-dimensional Artin groups [Vas20].…”
Section: Introduction Hyperbolic Features Of Artin Groupsmentioning
confidence: 99%