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Lattices, injective metrics and the $K(\pi,1)$ conjecture

Thomas Haettel

Algebraic & Geometric Topology 24 (2024) 4007–4060
Bibliography
1 G Basso, Extending and improving conical bicombings, Enseign. Math. 70 (2024) 165 MR4746040
2 D Bessis, A dual braid monoid for the free group, J. Algebra 302 (2006) 55 MR2236594
3 J Birman, K H Ko, S J Lee, A new approach to the word and conjugacy problems in the braid groups, Adv. Math. 139 (1998) 322 MR1654165
4 M A Blufstein, L Paris, Parabolic subgroups inside parabolic subgroups of Artin groups, Proc. Amer. Math. Soc. 151 (2023) 1519 MR4550347
5 N Bourbaki, Lie groups and Lie algebras, chapters IV–VI, Springer (2002) MR1890629
6 B H Bowditch, Median and injective metric spaces, Math. Proc. Cambridge Philos. Soc. 168 (2020) 43 MR4043820
7 T Brady, J McCammond, Braids, posets and orthoschemes, Algebr. Geom. Topol. 10 (2010) 2277 MR2745672
8 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
9 F Bruhat, J Tits, Groupes réductifs sur un corps local, Inst. Hautes Études Sci. Publ. Math. 41 (1972) 5 MR327923
10 J Chalopin, V Chepoi, A Genevois, H Hirai, D Osajda, Helly groups, preprint (2020) arXiv:2002.06895
11 J Chalopin, V Chepoi, H Hirai, D Osajda, Weakly modular graphs and nonpositive curvature, 1309, Amer. Math. Soc. (2020) MR4223822
12 R Charney, Geodesic automation and growth functions for Artin groups of finite type, Math. Ann. 301 (1995) 307 MR1314589
13 R Charney, The Deligne complex for the four-strand braid group, Trans. Amer. Math. Soc. 356 (2004) 3881 MR2058510
14 R Charney, Problems related to Artin groups, preprint (2008)
15 R Charney, M W Davis, Finite K(π,1)s for Artin groups, from: "Prospects in topology", Ann. of Math. Stud. 138, Princeton Univ. Press (1995) 110 MR1368655
16 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
17 J Crisp, Symmetrical subgroups of Artin groups, Adv. Math. 152 (2000) 159 MR1762124
18 M Cumplido, The conjugacy stability problem for parabolic subgroups in Artin groups, Mediterr. J. Math. 19 (2022) 237 MR4484940
19 M Cumplido, V Gebhardt, J González-Meneses, B Wiest, On parabolic subgroups of Artin–Tits groups of spherical type, Adv. Math. 352 (2019) 572 MR3964156
20 P Dehornoy, L Paris, Gaussian groups and Garside groups, two generalisations of Artin groups, Proc. Lond. Math. Soc. 79 (1999) 569 MR1710165
21 P Dehornoy, F Digne, E Godelle, D Krammer, J Michel, Foundations of Garside theory, 22, Eur. Math. Soc. (2015) MR3362691
22 P Deligne, Les immeubles des groupes de tresses généralisés, Invent. Math. 17 (1972) 273 MR422673
23 D Descombes, U Lang, Flats in spaces with convex geodesic bicombings, Anal. Geom. Metr. Spaces 4 (2016) 68 MR3483604
24 F Digne, A Garside presentation for Artin–Tits groups of type Cn, Ann. Inst. Fourier (Grenoble) 62 (2012) 641 MR2985512
25 M Dougherty, J McCammond, S Witzel, Boundary braids, Algebr. Geom. Topol. 20 (2020) 3505 MR4194287
26 A W M Dress, Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: a note on combinatorial properties of metric spaces, Adv. Math. 53 (1984) 321 MR753872
27 E Godelle, Artin–Tits groups with CAT(0) Deligne complex, J. Pure Appl. Algebra 208 (2007) 39 MR2269827
28 E Godelle, L Paris, Basic questions on Artin–Tits groups, from: "Configuration spaces", CRM Series 14, Ed. Norm. (2012) 299 MR3203644
29 T Haettel, Injective metrics on buildings and symmetric spaces, Bull. Lond. Math. Soc. 54 (2022) 2297 MR4528624
30 T Haettel, A link condition for simplicial complexes, and CUB spaces, preprint (2022) arXiv:2211.07857
31 T Haettel, D Kielak, P Schwer, The 6–strand braid group is CAT(0), Geom. Dedicata 182 (2016) 263 MR3500387
32 T Haettel, N Hoda, H Petyt, Coarse injectivity, hierarchical hyperbolicity and semihyperbolicity, Geom. Topol. 27 (2023) 1587 MR4602421
33 N Hoda, Crystallographic Helly groups, Bull. Lond. Math. Soc. 55 (2023) 2991 MR4698324
34 J Huang, D Osajda, Helly meets Garside and Artin, Invent. Math. 225 (2021) 395 MR4285138
35 S G Jeong, The seven-strand braid group is CAT(0), Manuscripta Math. 171 (2023) 563 MR4597707
36 D Kasprowski, H Rüping, The Farrell–Jones conjecture for hyperbolic and CAT(0)–groups revisited, J. Topol. Anal. 9 (2017) 551 MR3684616
37 U Lang, Injective hulls of certain discrete metric spaces and groups, J. Topol. Anal. 5 (2013) 297 MR3096307
38 I J Leary, A Minasyan, Commensurating HNN extensions : nonpositive curvature and biautomaticity, Geom. Topol. 25 (2021) 1819 MR4286364
39 H van der Lek, The homotopy type of complex hyperplane complements, PhD thesis, Radboud University (1983)
40 J McCammond, An introduction to Garside structures, preprint (2006)
41 J McCammond, The mysterious geometry of Artin groups, Winter Braids Lect. Notes 4 (2017) 1 MR3922033
42 J McCammond, R Sulway, Artin groups of Euclidean type, Invent. Math. 210 (2017) 231 MR3698343
43 J Michel, A note on words in braid monoids, J. Algebra 215 (1999) 366 MR1684142
44 B Miesch, Injective metrics on cube complexes, preprint (2014) arXiv:1411.7234
45 B Miesch, The Cartan–Hadamard theorem for metric spaces with local geodesic bicombings, Enseign. Math. 63 (2017) 233 MR3777137
46 P Möller, L Paris, O Varghese, On parabolic subgroups of Artin groups, Israel J. Math. 261 (2024) 809 MR4775739
47 R Morris-Wright, Parabolic subgroups in FC-type Artin groups, J. Pure Appl. Algebra 225 (2021) 106468 MR4114975
48 L Nachbin, A theorem of the Hahn–Banach type for linear transformations, Trans. Amer. Math. Soc. 68 (1950) 28 MR32932
49 C Okonek, Das K(π, 1)–Problem für die affinen Wurzelsysteme vom Typ An,Cn, Math. Z. 168 (1979) 143 MR544701
50 D Osajda, M Valiunas, Helly groups, coarsely Helly groups, and relative hyperbolicity, Trans. Amer. Math. Soc. 377 (2024) 1505 MR4744735
51 G Paolini, M Salvetti, Proof of the K(π,1) conjecture for affine Artin groups, Invent. Math. 224 (2021) 487 MR4243019
52 J Światkowski, Regular path systems and (bi)automatic groups, Geom. Dedicata 118 (2006) 23 MR2239447
53 J Tits, Normalisateurs de tores, I : Groupes de Coxeter étendus, J. Algebra 4 (1966) 96 MR206117
54 J Tits, Buildings of spherical type and finite BN-pairs, 386, Springer (1974) MR470099