A note on some classical results of Gromov-Lawson
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Abstract:
In this paper we show how the higher index theory can be used to prove results concerning the non-existence of a complete Riemannian metric with uniformly positive scalar curvature at infinity. By improving some classical results due to M. Gromov and B. Lawson we show the efficiency of these methods to prove such non-existence theorems.References
- Saad Baaj, Calcul pseudo-différentiel et produits croisés de $C^*$-algèbres. I, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 11, 581–586 (French, with English summary). MR 967366
- Mikhael Gromov and H. Blaine Lawson Jr., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math. 58 (1983), 83–196 (1984). MR 720933
- B. Hanke and T. Schick, Enlargeability and index theory, J. Differential Geom. 74 (2006), no. 2, 293–320. MR 2259056
- Bernhard Hanke and Thomas Schick, Enlargeability and index theory: infinite covers, $K$-Theory 38 (2007), no. 1, 23–33. MR 2353861, DOI 10.1007/s10977-007-9004-3
- Nigel Higson, A note on the cobordism invariance of the index, Topology 30 (1991), no. 3, 439–443. MR 1113688, DOI 10.1016/0040-9383(91)90024-X
- Dan Kucerovsky, Functional calculus and representations of $C_0(\Bbb C)$ on a Hilbert module, Q. J. Math. 53 (2002), no. 4, 467–477. MR 1949157, DOI 10.1093/qjmath/53.4.467
- Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972. MR 0493419
- 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
- Jonathan Rosenberg, $C^{\ast }$-algebras, positive scalar curvature, and the Novikov conjecture, Inst. Hautes Études Sci. Publ. Math. 58 (1983), 197–212 (1984). MR 720934
- Mostafa Esfahani Zadeh, Index theory and partitioning by enlargeable hypersurfaces, J. Noncommut. Geom. 4 (2010), no. 3, 459–473. MR 2670972, DOI 10.4171/JNCG/63
Additional Information
- Mostafa Esfahani Zadeh
- Affiliation: Department of Mathematical Science, Sharif University of Technology, Tehran, Iran – and – School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran
- Email: esfahani@sharif.edu
- Received by editor(s): December 23, 2009
- Received by editor(s) in revised form: April 4, 2011
- Published electronically: March 5, 2012
- Additional Notes: This research was in part supported by a grant from IPM (No. 89510130).
- Communicated by: Varghese Mathai
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3663-3672
- MSC (2000): Primary 58J22; Secondary 19K56, 46L80, 53C21, 53C27
- DOI: https://doi.org/10.1090/S0002-9939-2012-11544-8
- MathSciNet review: 2929034