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Weighted sheaves and homology of Artin groups

Giovanni Paolini and Mario Salvetti

Algebraic & Geometric Topology 18 (2018) 3943–4000
Bibliography
1 I Agol, The virtual Haken conjecture, Doc. Math. 18 (2013) 1045 MR3104553
2 V Arnold, The cohomology ring of the colored braid group, Mat. Zametki 5 (1969) 227 MR0242196
3 V I Arnold, On some topological invariants of algebrac functions, Trudy Moskov. Mat. Obšč. 21 (1970) 27 MR0274462
4 E Babson, D N Kozlov, Proof of the Lovász conjecture, Ann. of Math. 165 (2007) 965 MR2335799
5 A Björner, F Brenti, Combinatorics of Coxeter groups, 231, Springer (2005) MR2133266
6 N Bourbaki, Éléments de mathématique, XXXIV : Groupes et algèbres de Lie, 1337, Hermann (1968) MR0240238
7 E Brieskorn, Sur les groupes de tresses (d’après V I Arnold), from: "Séminaire Bourbaki, 1972/1973", Lecture Notes in Math. 317, Springer (1973) 21 MR0422674
8 E Brieskorn, K Saito, Artin-Gruppen und Coxeter-Gruppen, Invent. Math. 17 (1972) 245 MR0323910
9 F Callegaro, On the cohomology of Artin groups in local systems and the associated Milnor fiber, J. Pure Appl. Algebra 197 (2005) 323 MR2123992
10 F Callegaro, The homology of the Milnor fiber for classical braid groups, Algebr. Geom. Topol. 6 (2006) 1903 MR2263054
11 F Callegaro, D Moroni, M Salvetti, Cohomology of affine Artin groups and applications, Trans. Amer. Math. Soc. 360 (2008) 4169 MR2395168
12 F Callegaro, D Moroni, M Salvetti, Cohomology of Artin groups of type Ãn, Bn and applications, from: "Groups, homotopy and configuration spaces" (editors N Iwase, T Kohno, R Levi, D Tamaki, J Wu), Geom. Topol. Monogr. 13, Geom. Topol. Publ. (2008) 85 MR2508202
13 F Callegaro, D Moroni, M Salvetti, The K(π,1) problem for the affine Artin group of type Bn and its cohomology, J. Eur. Math. Soc. 12 (2010) 1 MR2578601
14 F Callegaro, M Salvetti, Integral cohomology of the Milnor fibre of the discriminant bundle associated with a finite Coxeter group, C. R. Math. Acad. Sci. Paris 339 (2004) 573 MR2111354
15 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
16 F R Cohen, The homology of Cn+1–spaces, n 0, from: "The homology of iterated loop spaces", Lecture Notes in Mathematics 533, Springer (1976) 207 MR0436146
17 J Curry, R Ghrist, V Nanda, Discrete Morse theory for computing cellular sheaf cohomology, Found. Comput. Math. 16 (2016) 875 MR3529128
18 C De Concini, C Procesi, M Salvetti, Arithmetic properties of the cohomology of braid groups, Topology 40 (2001) 739 MR1851561
19 C De Concini, C Procesi, M Salvetti, F Stumbo, Arithmetic properties of the cohomology of Artin groups, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 28 (1999) 695 MR1760537
20 C De Concini, M Salvetti, Cohomology of Artin groups, Math. Res. Lett. 3 (1996) 293 MR1386847
21 P Deligne, Les immeubles des groupes de tresses généralisés, Invent. Math. 17 (1972) 273 MR0422673
22 A Engström, Complexes of directed trees and independence complexes, Discrete Math. 309 (2009) 3299 MR2526748
23 R Forman, Morse theory for cell complexes, Adv. Math. 134 (1998) 90 MR1612391
24 R Fox, L Neuwirth, The braid groups, Math. Scand. 10 (1962) 119 MR0150755
25 È V Frenkel, Cohomology of the commutator subgroup of the braid group, Funktsional. Anal. i Prilozhen. 22 (1988) 91 MR961774
26 D B Fuks, Cohomology of the braid group mod 2, Funkcional. Anal. i Priložen. 4 (1970) 62 MR0274463
27 V V Gorjunov, The cohomology of braid groups of series C and D and certain stratifications, Funktsional. Anal. i Prilozhen. 12 (1978) 76 MR498905
28 H Hendriks, Hyperplane complements of large type, Invent. Math. 79 (1985) 375 MR778133
29 J Jonsson, Simplicial complexes of graphs, 1928, Springer (2008) MR2368284
30 D Kozlov, Combinatorial algebraic topology, 21, Springer (2008) MR2361455
31 H v d Lek, The homotopy type of complex hyperplane complements, PhD thesis, Katholieke Universiteit te Nijmegen (1983)
32 D Moroni, M Salvetti, A Villa, Some topological problems on the configuration spaces of Artin and Coxeter groups, from: "Configuration spaces" (editors A Bjorner, F Cohen, C De Concini, C Procesi, M Salvetti), CRM Series 14, Ed. Norm. (2012) 403 MR3203650
33 C Okonek, Das K(π,1)–Problem für die affinen Wurzelsysteme vom Typ An,Cn, Math. Z. 168 (1979) 143 MR544701
34 V Ozornova, Discrete Morse theory and a reformulation of the K(π,1)–conjecture, Comm. Algebra 45 (2017) 1760 MR3576693
35 G Paolini, On the classifying space of Artin monoids, Comm. Algebra 45 (2017) 4740 MR3670346
36 G Paolini, On the local homology of Artin groups of finite and affine type, preprint (2017) arXiv:1709.01358
37 L Paris, K(π,1) conjecture for Artin groups, Ann. Fac. Sci. Toulouse Math. 23 (2014) 361 MR3205598
38 M Salvetti, Topology of the complement of real hyperplanes in N, Invent. Math. 88 (1987) 603 MR884802
39 M Salvetti, The homotopy type of Artin groups, Math. Res. Lett. 1 (1994) 565 MR1295551
40 M Salvetti, Some combinatorial constructions and relations with Artin groups, from: "Combinatorial methods in topology and algebra" (editors B Benedetti, E Delucchi, L Moci), Springer INdAM 12, Springer (2015) 121 MR3467336
41 M Salvetti, A Villa, Combinatorial methods for the twisted cohomology of Artin groups, Math. Res. Lett. 20 (2013) 1157 MR3228628
42 C C Squier, The homological algebra of Artin groups, Math. Scand. 75 (1994) 5 MR1308935
43 È B Vinberg, Discrete linear groups that are generated by reflections, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971) 1072 MR0302779
44 F V Weinstein, Cohomologies of braid groups, Funktsional. Anal. i Prilozhen. 12 (1978) 72 MR498903