C * -algebras, positive scalar curvature, and the Novikov conjecture
Publications Mathématiques de l'IHÉS, Tome 58 (1983), pp. 197-212 
@article{PMIHES_1983__58__197_0,
     author = {Rosenberg, Jonathan},
     title = {$C^\ast $-algebras, positive scalar curvature, and the {Novikov} conjecture},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {197--212},
     year = {1983},
     publisher = {Institut des Hautes Etudes Scientifiques},
     volume = {58},
     mrnumber = {85g:58083},
     zbl = {0526.53044},
     language = {en},
     url = {https://www.numdam.org/item/PMIHES_1983__58__197_0/}
}
TY  - JOUR
AU  - Rosenberg, Jonathan
TI  - $C^\ast $-algebras, positive scalar curvature, and the Novikov conjecture
JO  - Publications Mathématiques de l'IHÉS
PY  - 1983
SP  - 197
EP  - 212
VL  - 58
PB  - Institut des Hautes Etudes Scientifiques
UR  - https://www.numdam.org/item/PMIHES_1983__58__197_0/
LA  - en
ID  - PMIHES_1983__58__197_0
ER  - 
%0 Journal Article
%A Rosenberg, Jonathan
%T $C^\ast $-algebras, positive scalar curvature, and the Novikov conjecture
%J Publications Mathématiques de l'IHÉS
%D 1983
%P 197-212
%V 58
%I Institut des Hautes Etudes Scientifiques
%U https://www.numdam.org/item/PMIHES_1983__58__197_0/
%G en
%F PMIHES_1983__58__197_0
Rosenberg, Jonathan. $C^\ast $-algebras, positive scalar curvature, and the Novikov conjecture. Publications Mathématiques de l'IHÉS, Tome 58 (1983), pp. 197-212. https://www.numdam.org/item/PMIHES_1983__58__197_0/

[1] J. F. Adams, Infinite Loop Spaces, Annals of Math. Studies, no. 90, Princeton, Princeton Univ. Press, 1978. | Zbl | MR

[2] M. F. Atiyah, Vector bundles and the Künneth formula, Topology 1 (1962), 245-248. | Zbl | MR

[3] M. F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Astérisque, no. 32-33 (1976), 43-72. | Zbl | Numdam

[4] M. F. Atiyah and I. M. Singer, The index of elliptic operators : III, Ann. of Math. (2) 87 (1968), 546-604. | Zbl | MR

[5] M. F. Atiyah and I. M. Singer, The index of elliptic operators : IV, Ann. of Math. (2) 93 (1971), 119-138. | Zbl | MR

[6] S. E. Cappell, On homotopy invariance of higher signatures, Invent. Math. 33 (1976), 171-179. | Zbl | MR

[7] A. Connes and G. Skandalis, Théorème de l'indice pour les feuilletages, C. R. Acad. Sci. Paris, Sér. I, 292 (1981), 871-876. | Zbl | MR

[8] J. Cuntz, The K-groups for free products of C*-algebras, in Operator Algebras and Applications, R. V. KADISON, ed., Proc. Symp. Pure Math., vol. 38, Amer. Math. Soc., Providence, R. I., 1982, Part I, 81-84. | Zbl | MR

[9] M. Gromov and H. B. Lawson, Jr., Spin and scalar curvature in the presence of a fundamental group, I, Ann. of Math. (2), 111 (1980), 209-230. | Zbl | MR

[10] M. Gromov and H. B. Lawson, Jr., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, this volume, 83-196. | Zbl | Numdam

[11] N. Hitchin, Harmonic spinors, Adv. in Math. 14 (1974), 1-55. | Zbl | MR

[12] W. C. Hsiang and H. D. Rees, Miščenko's work on Novikov's conjecture, in Operator Algebras and K-Theory, | Zbl

R. G. Douglas and C. Schochet, eds., Contemporary Math., vol. 10, Amer. Math. Soc., Providence, R. I., 1982, 77-98. | MR

[13] M. Karoubi, K-Theory: An Introduction, Grundlehren der math. Wissenschaften, no. 226, Heidelberg and New York, Springer-Verlag, 1978. | Zbl | MR

[14] G. G. Kasparov, Topological invariants of elliptic operators, I: K-homology, Izv. Akad. Nauk SSSR, Ser. Mat. 39 (1975), 796-838 = Math. USSR-Izv. 9 (1975), 751-792. | Zbl | MR

[15] G. G. Kasparov, Hilbert C*-modules : theorems of Stinespring and Voiculescu, J. Operator Theory 4 (1980), 133-150. | Zbl | MR

[16] G. G. Kasparov, The operator K-functor and extensions of C*-algebras, Izv. Akad. Nauk SSSR, Ser. Mat. 44 (1980), 571-636 = Math. USSR-Izv. 16 (1981), 513-572. | Zbl | MR

[17] G. G. Kasparov, K-theory group C*-algebras, and higher signatures (conspectus), preprint, Chernogolovka, 1981.

[18] J. L. Kazdan and F. W. Warner, Scalar curvature and conformal deformation of Riemannian structure, J. Differential Geometry 10 (1975), 113-134. | Zbl | MR

[19] A. Lichnerowicz, Spineurs harmoniques, C. R. Acad. Sci. Paris, Sér. A-B 257 (1963), 7-9. | Zbl | MR

[20] J. Milnor, On axiomatic homology theory, Pacific J. Math. 12 (1962), 337-341. | Zbl | MR

[21] J. A. Mingo, K-theory and multipliers of stable C*-algebras, Ph. D. Thesis, Halifax, N.S., Dalhousie Univ., 1982. | Zbl

[22] A. S. Miščenko, C*-algebras and K-theory, in Algebraic Topology, Aarhus 1978, J. L. DUPONT and H. MADSEN, eds., Lecture Notes in Math., no. 763, Heidelberg and New York, Springer-Verlag, 1979, 262-274. | Zbl

[23] A. S. Miščenko and A. T. Fomenko, The index of elliptic operators avec C*-algebras, Izv. Akad. Nauk SSSR, Ser. Mat. 43 (1979), 831-859 = Math. USSR-Izv. 15 (1980), 87-112. | Zbl

[24] A. S. Miščenko and J. P. Solov'Ev, On infinite-dimensional representations of fundamental groups and formulas of Hirzebruch type, Dokl. Akad. Nauk SSSR 234 (1977), 761-764 = Soviet Math. Dokl. 18 (1977), 767-771. | Zbl | MR

[25] M. Pimsner and D. Voiculescu, Exact sequences for K-groups and Ext-groups of certain cross-product C*-algebras, J. Operator Theory 4 (1980), 93-118. | Zbl | MR

[26] J. Rosenberg, Group C*-algebras and topological invariants, in Operator Algebras and Group Representations, Proc. Conf. in Neptun, Romania, 1980, London, Pitman, 1983, to appear.

[27] C. Schochet, Topological methods for C*-algebras, II: geometric resolutions and the Künneth formula, Pacific J. Math. 98 (1982), 443-458. | Zbl | MR

[28] W. Shih, Fiber cobordism and the index of a family of elliptic differential operators, Bull. Amer. Math. Soc. 72 (1966), 984-991. | Zbl | MR