Abstract
Let M be an n-dimensional manifold (all manifolds considered in this paper are smooth, compact, and, unless otherwise specified, their boundary is empty).
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References
D. W. Anderson, E. H. Brown, Jr., and F. P. Peterson, Pin cobordism and related topics, Comment. Math. Helv. 44 (1969), 462–468.
A. L. Besse, Einstein Manifolds, Springer-Verlag, Berlin and New York, 1986.
B. Botvinnik and P. B. Gilkey, The eta invariant and metrics of positive scalar curvature, preprint.
B. Botvinnik, P. B. Gilkey, and S. Stolz, The Gromov-Lawson-Rosenberg Conjecture for space form qroups, preprint 1994.
U. Bunke, A K-theoretic relative index theorem and Callias-type Dirac operators, to appear in Math. Ann.
P. Gajer, Riemannian metrics of positive scalar curvature on compact manifolds with boundary, Ann. Global Anal. Geom. 5 (1987), 179–191.
M. Gromov and H. B. Lawson, Jr., The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. (2) 111 (1980), 423–434.
——, Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. IHES (1983), no. 58, 83–196.
B. Hajduk, On the obstruction group to the existence of Riemannian metrics of positive scalar curvature, Proc. International Conf. on Algebraic Topology, Poznan 1989, S. Jackowski, R. Oliver, and K. Pawalowski, eds., Lecture Notes in Math., Springer-Verlag, Berlin and New York, pp. 62–72.
N. Hitchin, Harmonic spinors, Adv. in Math. 14 (1974), 1–55.
R. Jung, Ph.D. thesis, Univ. of Mainz, Germany, in preparation.
G. G. Kasparov, Equivariant KK-theory and the Novikov Conjecture, Invent. Math. 91 (1988), 147–201.
M. Kreck and S. Stolz, HP 2 -bundles and elliptic homology, Acta Mathematica 171 (1993), 231–261.
S. Kwasik and R. Schultz, Positive scalar curvature and periodic fundamental groups, Comment. Math. Helv. 65 (1990), 271–286.
H. B. Lawson and M.-L. Michelsohn, Spin geometry, Princeton Mathematical Series, 38, Princeton Univ. Press, Princeton, NJ, 1989.
A. Lichnerowicz, Spineurs harmoniques, C. R. Acad. Sci. Paris, Série A-B 257 (1963), 7–9.
J. Rosenberg, C*-algebras, positive scalar curvature, and the Novikov Conjecture, II, Geometric Methods in Operator Algebras, H. Araki and E.G. Effros, eds., Pitman Research Notes in Math., no. 123, Longman/Wiley, Harlow, Essex, England and New York, 1986, pp. 341–374.
——, C*-algebras, positive scalar curvature, and the Novikov Conjecture, III, Topology 25 (1986), 319–336.
J. Rosenberg and S. Stolz, Manifolds of positive scalar curvature, Algebraic Topology and its Applications (G. Carlsson, R. Cohen, W.-C. Hsiang, and J.D.S. Jones, eds.), M. S. R. I. Publications, vol. 27, Springer-Verlag, Berlin and New York, 1994, pp. 241–267.
——, A “stable” version of the Gromov-Lawson conjecture, to appear in the Proc. of the Cech Centennial Homotopy Theory Conference, Cont. Math. 181 (1995), 405–418.
——, The stable classification of manifolds of positive scalar curvature, in preparation.
R. Schoen and S.-T. Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), 159–183.
S. Stolz, Simply connected manifolds of positive scalar curvature, Ann. of Math. (2) 136 (1992), 511–540.
——, Splitting certain MSpin-module spectra, Topology 33 (1994), 159–180.
——, Concordance classes of positive scalar curvature metrics, in preparation.
C.T.C. Wall, Surgery on compact manifolds, Academic Press, London and New York. 1970.
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© 1995 Birkhäser Verlag, Basel, Switzerland
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Stolz, S. (1995). Positive Scalar Curvature Metrics — Existence and Classification Questions. In: Chatterji, S.D. (eds) Proceedings of the International Congress of Mathematicians. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-9078-6_56
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DOI: https://doi.org/10.1007/978-3-0348-9078-6_56
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