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Weighted $L^2$–cohomology of Coxeter groups

Michael W Davis, Jan Dymara, Tadeusz Januszkiewicz and Boris Okun

Geometry & Topology 11 (2007) 47–138
Bibliography
1 E M Andreev, Convex polyhedra in Lobačevskiĭ spaces, Mat. Sb. $($N.S.$)$ 81 (123) (1970) 445 MR0259734
2 E M Andreev, Convex polyhedra of finite volume in Lobačevskiĭ space, Mat. Sb. $($N.S.$)$ 83 (125) (1970) 256 MR0273510
3 D Boros, $\ell^2$-homology of low dimensional buildings, PhD thesis, The Ohio State University (2003)
4 N Bourbaki, Lie groups and Lie algebras. Chapters 4–6, Elements of Mathematics (Berlin), Springer (2002) MR1890629
5 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften, Springer (1999) MR1744486
6 A Brøndsted, An introduction to convex polytopes, Graduate Texts in Mathematics 90, Springer (1983) MR683612
7 K S Brown, Buildings, Springer (1989) MR969123
8 E L Bueler, The heat kernel weighted Hodge Laplacian on noncompact manifolds, Trans. Amer. Math. Soc. 351 (1999) 683 MR1443866
9 R Charney, M Davis, Reciprocity of growth functions of Coxeter groups, Geom. Dedicata 39 (1991) 373 MR1123152
10 J Cheeger, M Gromov, Bounds on the von Neumann dimension of $L^2$-cohomology and the Gauss-Bonnet theorem for open manifolds, J. Differential Geom. 21 (1985) 1 MR806699
11 J Cheeger, M Gromov, $L_2$-cohomology and group cohomology, Topology 25 (1986) 189 MR837621
12 M W Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. $(2)$ 117 (1983) 293 MR690848
13 M W Davis, The homology of a space on which a reflection group acts, Duke Math. J. 55 (1987) 97 MR883665
14 M W Davis, Buildings are $\mathrm{CAT}(0)$, from: "Geometry and cohomology in group theory (Durham, 1994)", London Math. Soc. Lecture Note Ser. 252, Cambridge Univ. Press (1998) 108 MR1709955
15 M W Davis, The cohomology of a Coxeter group with group ring coefficients, Duke Math. J. 91 (1998) 297 MR1600586
16 M W Davis, Nonpositive curvature and reflection groups, from: "Handbook of geometric topology", North-Holland (2002) 373 MR1886674
17 M W Davis, The Geometry and Topology of Coxeter Groups, London Math. Soc. Monograph Series, Princeton Univ. Press (in press)
18 M W Davis, J Dymara, T Januszkiewicz, B Okun, Cohomology of Coxeter groups with group ring coefficients. II, Algebr. Geom. Topol. 6 (2006) 1289 MR2253447
19 M W Davis, I J Leary, The $l^2$-cohomology of Artin groups, J. London Math. Soc. $(2)$ 68 (2003) 493 MR1994696
20 M W Davis, J Meier, The topology at infinity of Coxeter groups and buildings, Comment. Math. Helv. 77 (2002) 746 MR1949112
21 M W Davis, B Okun, Vanishing theorems and conjectures for the $\ell^2$-homology of right-angled Coxeter groups, Geom. Topol. 5 (2001) 7 MR1812434
22 M W Davis, B Okun, $l^2$-homology of right-angled Coxeter groups based on barycentric subdivisions, Topology Appl. 140 (2004) 197 MR2074916
23 J Dixmier, Les $C_{*}$–algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris (1964) MR0171173
24 J Dixmier, von Neumann algebras, North-Holland Mathematical Library 27, North-Holland Publishing Co. (1981) MR641217
25 J Dodziuk, de Rham-Hodge theory for $L^{2}$-cohomology of infinite coverings, Topology 16 (1977) 157 MR0445560
26 J Dymara, $L^2$-cohomology of buildings with fundamental class, Proc. Amer. Math. Soc. 132 (2004) 1839 MR2051148
27 J Dymara, Thin buildings, Geom. Topol. 10 (2006) 667 MR2240901
28 J Dymara, T Januszkiewicz, Cohomology of buildings and their automorphism groups, Invent. Math. 150 (2002) 579 MR1946553
29 B Eckmann, Introduction to $l_2$-methods in topology: reduced $l_2$-homology, harmonic chains, $l_2$-Betti numbers, Israel J. Math. 117 (2000) 183 MR1760592
30 Ś R Gal, Real root conjecture fails for five- and higher-dimensional spheres, Discrete Comput. Geom. 34 (2005) 269 MR2155722
31 C Gonciulea, Virtual epimorphisms of Coxeter groups onto free groups, PhD thesis, The Ohio State University (2000)
32 D Kazhdan, G Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979) 165 MR560412
33 W Lück, $L^2$–invariants: theory and applications to geometry and $K$–theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer (2002) MR1926649
34 G Lusztig, Left cells in Weyl groups, from: "Lie group representations, I (College Park, Md., 1982/1983)", Lecture Notes in Math. 1024, Springer (1983) 99 MR727851
35 G A Margulis, È B Vinberg, Some linear groups virtually having a free quotient, J. Lie Theory 10 (2000) 171 MR1748082
36 G Moussong, Hyperbolic Coxeter groups, PhD thesis, The Ohio State University (1998)
37 M Ronan, Lectures on buildings, Perspectives in Mathematics 7, Academic Press (1989) MR1005533
38 J P Serre, Cohomologie des groupes discrets, from: "Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970)", Princeton Univ. Press (1971) MR0385006
39 L Solomon, A decomposition of the group algebra of a finite Coxeter group, J. Algebra 9 (1968) 220 MR0232868
40 R Steinberg, Endomorphisms of linear algebraic groups, Memoirs of the American Mathematical Society 80, American Mathematical Society (1968) 108 MR0230728
41 J Tits, Le problème des mots dans les groupes de Coxeter, from: "Symposia Mathematica (INDAM, Rome, 1967/68), Vol. 1", Academic Press (1969) 175 MR0254129
42 C A Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics 38, Cambridge University Press (1994) MR1269324