Vanishing theorems and conjectures for the ℓ2-homology of right-angled Coxeter groups

Geometry and Topology

Volumn 5, Issue , 2001, Pages 7-74

  Davis, Michael W ^a   Okun, Boris ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

Aspherical manifold; Coxeter group; Nonpositive curvature; 2 Betti numbers; 2 homology

Indexed keywords

EID: 0011040168     PISSN: 14653060     EISSN: None     Source Type: Journal    
DOI: 10.2140/gt.2001.5.7     Document Type: Article

References (39)

1. T Akita, Euler characteristics of Coxeter groups, PL-triangulations of closed manifolds, and cohomology of subgroups of Artin groups, J. London Math. Soc. (2) 61 (2000) 721-736
2. E M Andreev, On convex polyhedra in Lobačevskiǐ spaces, Math.USSR Sb. 10 (1970) 413-440
3. E M Andreev, On convex polyhedra of finite volume in Lobač evskiǐ space, Math.USSR Sb. 12 (1970) 255-259
4. M F Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Soc. Math. France, Paris (1976) 43-72. Astérisque, No. 32-33
5. M Bestvina, M Kapovich, B Kleiner, Van Kampen's embedding obstruction for discrete groups, in preparation
6. N Bourbaki, Éléments de mathématique, Groupes et algèbres de Lie, Chapitres 4, 5 et 6 , Masson, Paris (1981)
7. G E Bredon, Sheaf theory, Springer, New York, second edition (1997)
8. M Bridson, A Haefliger, Metric Spaces of Nonpositive Curvature, Springer, New York (1999)
9. W Browder, Surgery on simply-connected manifolds, Springer, New York (1972), Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 65
10. R Charney, M Davis, The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold , Pacific J. Math. 171 (1995) 117-137
11. 2-cohomology and the Gauss-Bonnet theorem for open manifolds, J. Differential Geom. 21 (1985) 1-34
12. 2-cohomology and group cohomology, Topology 25 (1986) 189-215
13. J Cheeger, W Müller, R Schrader, On the curvature of piecewise flat spaces, Comm. Math. Phys. 92 (1984) 405-454
14. S S Chern, On curvature and characteristic classes of a Riemannian manifold , Abh. Math. Sem. 20 (1956) 117-126
15. M W Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. 117 (1983) 293-324
16. M W Davis, Coxeter groups and aspherical manifolds, in Algebraic topology, Aarhus 1982 (Aarhus, 1982), Springer, New York, volume 1051 of Lecture Notes in Math. (1984) 197-221
17. M W Davis, Nonpositive curvature and reflection groups, in R Daverman, R Sher (Eds.), Handbook of Geometric Topology, Elsevier, Amsterdam (to appear)
18. M Davis, T Januszkiewicz, R Scott, Nonpositive curvature of blow-ups, Selecta Math. (N.S.) 4 (1998) 491-547
19. M W Davis, G Moussong, Notes on nonpositively curved polyhedra, in Low dimensional topology (Eger, 1996/Budapest, 1998), János Bolyai Math. Soc., Budapest (1999) 11-94
20. 2-cohomology of infinite coverings, Topology 16 (1977) 157-165
21. 2 harmonic forms on rotationally symmetric Riemannian manifolds, Proc. Amer. Math. Soc. 77 (1979) 395-400
22. H Donnelly, F Xavier, On the differential form spectrum of negatively curved Riemannian manifolds, Amer. J. Math. 106 (1984) 169-185
23. 2-Betti numbers, Israel J. Math. 117 (2000) 183-219, notes prepared by Guido Mislin
24. M S Farber, Homological algebra of Novikov-Shubin invariants and Morse inequalities, Geom. Funct. Anal. 6 (1996) 628-665
25. M S Farber, von Neumann Betti nimbers and Novikov type inequalities, Proc. Amer. Math. Soc. (to appear)
26. M Gromov, Hyperbolic groups, in Essays in group theory, Springer, New York (1987) 75-263
27. 2-Hodge theory, J. Differential Geom. 33 (1991) 263-292
28. M Gromov, Asymptotic invariants of infinite groups, in Geometric group theory, Vol. 2 (Sussex, 1991), Cambridge Univ. Press, Cambridge (1993) 1-295
29. J L Gross, T W Tucker, Topological graph theory, John Wiley & Sons Inc., New York (1987), a Wiley-Interscience Publication
30. A Haefliger, Complexes of groups and orbihedra, in Group theory from a geometrical viewpoint (Trieste, 1990), World Sci. Publishing, River Edge, NJ (1991) 504-540
31. H Kesten, Full Banach mean values on countable groups, Math. Scand. 7 (1959) 146-156
32. 2-topological invariants of 3-manifolds, Invent. Math. 120 (1995) 15-60
33. 2-Betti numbers of mapping tori and groups, Topology 33 (1994) 203-214
34. J J Millson, On the first Betti number of a constant negatively curved manifold , Ann. of Math. 104 (1976) 235-247
35. G Moussong, Hyperbolic Coxeter groups, Ph.D. thesis, The Ohio State University (1988)
36. 1, in Bourbaki Seminar, Vol. 1979/80, Springer, New York, volume 842 of Lecture Notes in Math (1981) 196-214
37. W P Thurston, A norm for the homology of 3-manifolds, Mem. Amer. Math. Soc. 59 (1986) i-vi and 99-130
38. W P Thurston, Manuscript for continuation of The geometry and topology of three-manifolds (1990), Chapter 5: orbifolds and Seifert fiber spaces
39. C T C Wall, Rational Euler characteristics, Proc. Cambridge Philos. Soc. 57 (1961) 182-184