Algebraic & Geometric Topology Volume 24, issue 3 (2024)

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The $K(\pi,1)$ conjecture and acylindrical hyperbolicity for relatively extra-large Artin groups

Katherine M Goldman

Algebraic & Geometric Topology 24 (2024) 1487–1504

DOI: 10.2140/agt.2024.24.1487

Bibliography

1	K I Appel, P E Schupp, Artin groups and infinite Coxeter groups, Invent. Math. 72 (1983) 201 MR0700768
2	N Bourbaki, Lie groups and Lie algebras, Chapters 4–6, Springer (2002) MR1890629
3	B H Bowditch, Tight geodesics in the curve complex, Invent. Math. 171 (2008) 281 MR2367021
4	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
5	M Calvez, Euclidean Artin–Tits groups are acylindrically hyperbolic, Groups Geom. Dyn. 16 (2022) 963 MR4506543
6	M Calvez, B Wiest, Acylindrical hyperbolicity and Artin–Tits groups of spherical type, Geom. Dedicata 191 (2017) 199 MR3719080
7	R Charney, The Tits conjecture for locally reducible Artin groups, Int. J. Algebra Comput. 10 (2000) 783 MR1809385
8	R Charney, M W Davis, The K(π,1)–problem for hyperplane complements associated to infinite reflection groups, J. Amer. Math. Soc. 8 (1995) 597 MR1303028
9	I Chatterji, A Martin, A note on the acylindrical hyperbolicity of groups acting on CAT(0) cube complexes, from: "Beyond hyperbolicity" (editors M Hagen, R Webb, H Wilton), Lond. Math. Soc. Lect. Note Ser. 454, Cambridge Univ. Press (2019) 160 MR3966610
10	P Deligne, Les immeubles des groupes de tresses généralisés, Invent. Math. 17 (1972) 273 MR0422673
11	G Ellis, E Sköldberg, The K(π,1) conjecture for a class of Artin groups, Comment. Math. Helv. 85 (2010) 409 MR2595184
12	E Godelle, L Paris, K(π,1) and word problems for infinite type Artin–Tits groups, and applications to virtual braid groups, Math. Z. 272 (2012) 1339 MR2995171
13	A Haefliger, Extension of complexes of groups, Ann. Inst. Fourier (Grenoble) 42 (1992) 275 MR1162563
14	T Haettel, XXL type Artin groups are CAT(0) and acylindrically hyperbolic, Ann. Inst. Fourier (Grenoble) 72 (2022) 2541 MR4500363
15	A Juhász, Relatively extra-large Artin groups, Groups Geom. Dyn. 12 (2018) 1343 MR3874644
16	H van der Lek, The homotopy type of complex hyperplane complements, PhD thesis, Katholieke Universiteit Nijmegen (1983)
17	A Martin, On the acylindrical hyperbolicity of the tame automorphism group of SL₂(ℂ), Bull. Lond. Math. Soc. 49 (2017) 881 MR3742454
18	D Osin, Acylindrically hyperbolic groups, Trans. Amer. Math. Soc. 368 (2016) 851 MR3430352
19	G Paolini, M Salvetti, Proof of the K(π,1) conjecture for affine Artin groups, Invent. Math. 224 (2021) 487 MR4243019
20	L Paris, K(π,1) conjecture for Artin groups, Ann. Fac. Sci. Toulouse Math. 23 (2014) 361 MR3205598
21	N Vaskou, Acylindrical hyperbolicity for Artin groups of dimension 2, Geom. Dedicata 216 (2022) 7 MR4366944