@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},
volume = {58},
year = {1983},
pages = {197-212},
mrnumber = {85g:58083},
zbl = {0526.53044},
language = {en},
url = {http://dml.mathdoc.fr/item/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. http://gdmltest.u-ga.fr/item/PMIHES_1983__58__197_0/
[1] , Infinite Loop Spaces, Annals of Math. Studies, no. 90, Princeton, Princeton Univ. Press, 1978. | MR 80d:55001 | Zbl 0398.55008
[2] , Vector bundles and the Künneth formula, Topology 1 (1962), 245-248. | MR 27 #767 | Zbl 0108.17801
[3] , Elliptic operators, discrete groups and von Neumann algebras, Astérisque, no. 32-33 (1976), 43-72. | Zbl 0323.58015
[4] and , The index of elliptic operators : III, Ann. of Math. (2) 87 (1968), 546-604. | MR 38 #5245 | Zbl 0164.24301
[5] and , The index of elliptic operators : IV, Ann. of Math. (2) 93 (1971), 119-138. | MR 43 #5554 | Zbl 0212.28603
[6] , On homotopy invariance of higher signatures, Invent. Math. 33 (1976), 171-179. | MR 55 #11264 | Zbl 0335.57007
[7] and , Théorème de l'indice pour les feuilletages, C. R. Acad. Sci. Paris, Sér. I, 292 (1981), 871-876. | MR 82f:58079 | Zbl 0529.58030
[8] , 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. | MR 84f:46078 | Zbl 0502.46050
[9] and , , Spin and scalar curvature in the presence of a fundamental group, I, Ann. of Math. (2), 111 (1980), 209-230. | MR 81g:53022 | Zbl 0445.53025
[10] and , , Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, this volume, 83-196. | Numdam | Zbl 0538.53047
[11] , Harmonic spinors, Adv. in Math. 14 (1974), 1-55. | MR 50 #11332 | Zbl 0284.58016
[12] and , Miščenko's work on Novikov's conjecture, in Operator Algebras and K-Theory, | Zbl 0512.57007
and , eds., Contemporary Math., vol. 10, Amer. Math. Soc., Providence, R. I., 1982, 77-98. | MR 83d:46002
[13] , K-Theory: An Introduction, Grundlehren der math. Wissenschaften, no. 226, Heidelberg and New York, Springer-Verlag, 1978. | MR 58 #7605 | Zbl 0382.55002
[14] , 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. | MR 58 #7603 | Zbl 0337.58006
[15] , Hilbert C*-modules : theorems of Stinespring and Voiculescu, J. Operator Theory 4 (1980), 133-150. | MR 82b:46074 | Zbl 0456.46059
[16] , 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. | MR 81m:58075 | Zbl 0464.46054
[17] , K-theory group C*-algebras, and higher signatures (conspectus), preprint, Chernogolovka, 1981.
[18] and , Scalar curvature and conformal deformation of Riemannian structure, J. Differential Geometry 10 (1975), 113-134. | MR 51 #1661 | Zbl 0296.53037
[19] , Spineurs harmoniques, C. R. Acad. Sci. Paris, Sér. A-B 257 (1963), 7-9. | MR 27 #6218 | Zbl 0136.18401
[20] , On axiomatic homology theory, Pacific J. Math. 12 (1962), 337-341. | MR 28 #2544 | Zbl 0114.39604
[21] , K-theory and multipliers of stable C*-algebras, Ph. D. Thesis, Halifax, N.S., Dalhousie Univ., 1982. | Zbl 0616.46067
[22] , 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 0444.57014
[23] and , 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 0448.46039
[24] and , 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. | MR 58 #13219 | Zbl 0376.57017
[25] and , Exact sequences for K-groups and Ext-groups of certain cross-product C*-algebras, J. Operator Theory 4 (1980), 93-118. | MR 82c:46074 | Zbl 0474.46059
[26] , Group C*-algebras and topological invariants, in Operator Algebras and Group Representations, Proc. Conf. in Neptun, Romania, 1980, London, Pitman, 1983, to appear.
[27] , Topological methods for C*-algebras, II: geometric resolutions and the Künneth formula, Pacific J. Math. 98 (1982), 443-458. | MR 84g:46105b | Zbl 0439.46043
[28] , Fiber cobordism and the index of a family of elliptic differential operators, Bull. Amer. Math. Soc. 72 (1966), 984-991. | MR 34 #6804 | Zbl 0161.42902