Zero-in-the-spectrum conjecture, positive scalar curvature and asymptotic dimension

Inventiones Mathematicae

Volumn 127, Issue 1, 1996, Pages 99-126

  Yu, Guoliang ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031538694     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050116     Document Type: Article

References (39)

1. M. Atiyah: Elliptic operators, discrete groups and von Neumann algebras. Asterisque 32, 43-72 (1976)
2. P. Baum, A. Connes: K-theory for discrete groups. In: Evans and Takesaki, eds, Operator Algebras and Applications, pp. 1-19. Cambridge University Press (1989)
3. P. Baum, A. Connes, N. Higson: Classifying space for proper actions and K-theory of crossed-product C*-algebras. 1992. (Preprint)
4. P. Baum, R. G. Douglas: Relative K-homology and C*-algebras. K-Theory 5, 1-46 (1991)
5. B. Blackadar: K-theory for operator algebras. MSRI Publications. Springer Verlag, New York, 1986.
6. P.R. Chernof: Essential selfadjointness of powers of generators of hyperbolic equations. J. Functional Analysis 12, 401-414 (1973)
7. A. Connes: Non-commutative differential geometry. IHES 62, 41-144 (1985)
8. A. Connes: Cyclic cohomology and transverse fundamental class of a foliation. Geometric methods in operator algebras. Pitman Research Notes in Mathematics 123, 52-144 (1986)
9. 2-index theorem for homogeneous spaces of Lie groups. Ann. Math. (2) 115, 291-330 (1982)
10. A. Connes, H. Moscovici: Cyclic cohomology and Novikov conjecture and hyperbolic groups. Topology 29 (3), 345-388 (1990)
11. A. Connes, M. Gromov, H. Moscovici: Group cohomology with Lipschitz control and higher signature. Geometric and Func. Anal. 3 (1), 1-78 (1993)
12. M. Davis: Groups generated by reflections and aspherical manifolds not covered by Euclidean space. Ann. of Math. 117 (2), 293-325 (1983)
13. M. Gromov: Hyperbolic groups. Essays in group theory. In: S.M. Gersten, ed., MSRI Publication; 8. Springer, New York, pp. 75-264 (1987)
14. M. Gromov: Large Riemannian manifolds. Lecture Notes in Math. 1201, 108-122 (1985)
15. M. Gromov: Asymptotic invariants for infinite groups. Vol. 2. Proceedings of the 1991 Sussex Conference on Geometric Group Theory, LMS Lecture Notes Series 182, 1993
16. M. Gromov, H.B. Lawson: Spin and scalar curvature in the presence of a fundamental group. Ann. Math. 111, 209-230 (1980)
17. M. Gromov, H.B. Lawson: Positive scalar curvature and the Dirac operator. Publ. I.H.E.S. 58, 83-196 (1983)
18. N. Higson. K-homology and operators on noncompact manifolds. 1988. Preprint
19. N. Higson: On the relative K-homology theory of Baum and Douglas. 1989 (Preprint)
20. N. Higson, J. Roe, G. Yu: A coarse Mayer-Vietoris sequence. Math. Proc. Camb. Phil. Soc. 114, 85, 85-97 (1993)
21. N. Higson, J. Roe: The Baum-Connes conjecture in coarse geometry. In: S. Ferry, A. Ranicki, J. Rosenberg, eds, Proceedings of the 1993 Oberwolfach Conference on teh Novikov conjecture, LMS Lecture Notes Series 227, 227-254 (1995)
22. N. Higson, G. Yu: K-theory for covering spaces. 1992 (Preprint)
23. G.G. Kasparov: Equivariant KK-theory and the Novikov conjecture. Invent. Math. 91, 147-201 (1988)
24. G.G. Kasparov, G. Skandalis: Groups acting on buildings, operator K-theory, and Novikov's conjecture. K-Theory 4, 303-337 (1991)
25. H.B. Lawson, M.L. Michelson: Spin Geometry. Princeton University Press, Princeton, 1989
26. J.W. Milnor: Introduction to Algebraic K-Theory, Volume 72. Annals of Mathematics Studies. Princeton (1972)
27. A.S. Miscenko: Homotopy invariants of nonsimply connected manifolds. Rational invariants I. Izv. Akad. Nauk. SSSR 34 No. 3, 501-514 (1970)
28. A.S. Miscenko, A.T. Fomenko: The index of elliptic operators over C*-algebras. Izv. Akad. Nauk. SSSR, Ser. Mat. 43, 831-859 (1979)
29. M. Pimsner: KK-groups of groups of crossed products by groups acting on trees. Invent. Math. 86, 603-634 (1988)
30. J. Roe: An index theorem on open manifold. J. Differential Geometry 27, 87-113 (1988)
31. J. Roe: Exotic cohomology and index theory. Bull. Amer. Math. Soc. 23 (2), 447-453 (1990)
32. J. Roe: Coarse cohomology and index theory for complete Riemannian manifolds. Memoirs Amer. Math. Soc. No. 497 (1993)
33. J. Roe: Hyperbolic metric spaces and the exotic cohomology Novikov conjecture. K-Theory 4, 501-512 (1991)
34. J. Rosenberg: C*-algebras, positive scalar curvature and the Novikov conjecture. Publ. I.H.E.S. 58, 409-424 (1983)
35. G. Yu: K-theoretic indices of Dirac type operators on complete manifolds and the Roe algebra. 1991 (Preprint) To appear in K-Theory
36. G. Yu: Cyclic cohomology and higher indices for complete manifolds. J. of Functional Analysis 133, 442-473 (1995)
37. G. Yu: Baum-Connes conjecture and coarse geometry. K-Theory 9, 3, 223-231 (1995)
38. G. Yu: Coarse Baum-Connes conjecture. K-Theory 9, 3, 199-221 (1995)
39. G. Yu: Localization algebra and coarse Baum-Connes conjecture. 1994 (Preprint) To appear in K-Theory