Exotic cohomology and index theory
HTML articles powered by AMS MathViewer
References
- M. Atiyah, R. Bott, and V. K. Patodi, On the heat equation and the index theorem, Invent. Math. 19 (1973), 279–330. MR 650828, DOI 10.1007/BF01425417
- M. F. Atiyah and I. M. Singer, The index of elliptic operators. III, Ann. of Math. (2) 87 (1968), 546–604. MR 236952, DOI 10.2307/1970717
- B. Blackadar, Operator algebras, Encyclopaedia of Mathematical Sciences, vol. 122, Springer-Verlag, Berlin, 2006. Theory of $C^*$-algebras and von Neumann algebras; Operator Algebras and Non-commutative Geometry, III. MR 2188261, DOI 10.1007/3-540-28517-2 4. A. Connes, Non-commutative differential geometry, Publ. Math. l’Institut des Hautes Études Scientifiques 62 (1985), 141-144.
- Alain Connes and Henri Moscovici, Conjecture de Novikov et groupes hyperboliques, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 9, 475–480 (French, with English summary). MR 964110
- Alain Connes and Henri Moscovici, Cyclic cohomology, the Novikov conjecture and hyperbolic groups, Topology 29 (1990), no. 3, 345–388. MR 1066176, DOI 10.1016/0040-9383(90)90003-3
- Hans Freudenthal, Neuaufbau der Endentheorie, Ann. of Math. (2) 43 (1942), 261–279 (German). MR 6504, DOI 10.2307/1968869
- Ezra Getzler, Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem, Comm. Math. Phys. 92 (1983), no. 2, 163–178. MR 728863, DOI 10.1007/BF01210843
- Mikhael Gromov, Structures métriques pour les variétés riemanniennes, Textes Mathématiques [Mathematical Texts], vol. 1, CEDIC, Paris, 1981 (French). Edited by J. Lafontaine and P. Pansu. MR 682063 10. M. Gromov and H. B. Lawson, Positive scalar curvature and the Dirac operator, Publ. Math. l’Institut des Hautes Études Scientifiques 58 (1983), 83-196.
- Mikhael Gromov and H. Blaine Lawson Jr., Spin and scalar curvature in the presence of a fundamental group. I, Ann. of Math. (2) 111 (1980), no. 2, 209–230. MR 569070, DOI 10.2307/1971198 12. N. Higson, On the relative K-homology theory of Baum and Douglas, preprint, 1989.
- André Lichnerowicz, Spineurs harmoniques, C. R. Acad. Sci. Paris 257 (1963), 7–9 (French). MR 156292
- John Milnor, Introduction to algebraic $K$-theory, Annals of Mathematics Studies, No. 72, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. MR 0349811
- John Roe, Exotic cohomology and index theory, Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 2, 447–453. MR 1049433, DOI 10.1090/S0273-0979-1990-15956-7
- John Roe, An index theorem on open manifolds. I, II, J. Differential Geom. 27 (1988), no. 1, 87–113, 115–136. MR 918459
- John Roe, Operator algebras and index theory on noncompact manifolds, Index theory of elliptic operators, foliations, and operator algebras (New Orleans, LA/Indianapolis, IN, 1986) Contemp. Math., vol. 70, Amer. Math. Soc., Providence, RI, 1988, pp. 229–249. MR 948695, DOI 10.1090/conm/070/948695
- John Roe, Partitioning noncompact manifolds and the dual Toeplitz problem, Operator algebras and applications, Vol. 1, London Math. Soc. Lecture Note Ser., vol. 135, Cambridge Univ. Press, Cambridge, 1988, pp. 187–228. MR 996446, DOI 10.1016/0165-1781(88)90061-3
- R. Schoen and Shing Tung Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. (2) 110 (1979), no. 1, 127–142. MR 541332, DOI 10.2307/1971247
- R. Schoen and S. T. Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), no. 1-3, 159–183. MR 535700, DOI 10.1007/BF01647970
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
Additional Information
- Journal: Bull. Amer. Math. Soc. 23 (1990), 447-453
- MSC (1985): Primary 57G12; Secondary 19K56, 55N35
- DOI: https://doi.org/10.1090/S0273-0979-1990-15956-7
- MathSciNet review: 1049433