Surveys in Noncommutative Geometry: Proceedings from the Clay Mathematics Institute Instructional Symposium, Held in Conjuction with the AMS-IMS-SIAM Joint Summer Research Conference on Noncommutative Geometry, June 18-29, 2000, Mount Holyoke College, South Hadley, MANigel Higson, John Roe American Mathematical Soc., 2006 - 189 pages In June 2000, the Clay Mathematics Institute organized an Instructional Symposium on Noncommutative Geometry in conjunction with the AMS-IMS-SIAM Joint Summer Research Conference. These events were held at Mount Holyoke College in Massachusetts from June 18 to 29, 2000. The Instructional Symposium consisted of several series of expository lectures which were intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Those expository lectures have been edited and are reproduced in this volume. The lectures of Rosenberg and Weinberger discuss various applications of noncommutative geometry to problems in ``ordinary'' geometry and topology. The lectures of Lagarias and Tretkoff discuss the Riemann hypothesis and the possible application of the methods of noncommutative geometry in number theory. Higson gives an account of the ``residue index theorem'' of Connes and Moscovici. Noncommutative geometry is to an unusual extent the creation of a single mathematician, Alain Connes. The present volume gives an extended introduction to several aspects of Connes' work in this fascinating area. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA). |
Table des matières
A Minicourse on Applications of NonCommutative Geometry to Topology | 1 |
On NovikovType Conjectures | 43 |
The Residue Index Theorem of Connes and Moscovici | 71 |
Arithmetic and Geometry | 127 |
Noncommutative Geometry and Number Theory | 143 |
Expressions et termes fréquents
action Amer analytic assembly map Atiyah automorphisms B)-cocycle Baum-Connes conjecture Borel conjecture bounded operators bundle C*-algebra Chern character cocycle compact manifold complex computation cyclic cocycle cyclic cohomology defined DEFINITION denote differential operators dimension divisors element elliptic operators equation equivariant example explicit formula finite foliation Fredholm module function field fundamental group global field Hilbert space Hochschild homeomorphism homotopy equivalence idele index formula index theorem integral invertible isomorphism JLO cocycle L-functions LEMMA linear Math Mathematics metric multiplication Neumann algebra noncommutative geometry Novikov conjecture number field number theory operator on H periodic cyclic cohomology positive scalar curvature proof residue cocycle result Riemann hypothesis Riemann zeta function Riemannian scalar curvature Section signature space H spectral triple symmetry topology torsion trace formula trace-class universal cover vector von Neumann algebra zeros
Fréquemment cités
Page xiv - P. Baum, A. Connes, and N. Higson, Classifying space for proper actions and K-theory of group C' -algebras, C"-algebras: 1943-1993 (San Antonio, TX, 1993), Contemp.
Page xv - Essay on Physics and Non-commutative Geometry, The Interface of Mathematics and Particle Physics, Oxford, September 1988, Clarendon Press, Oxford, 1990.
Page xv - York, 1990, pp. 9-48. 12. A. Connes, Noncommutative geometry, Academic Press, 1994. 13. A. Connes, Noncommutative geometry and the Riemann zeta function, Mathematics: frontiers and perspectives, Amer.
Page xv - S. Hurder and A. Katok, Secondary classes and transverse measure theory of a foliation, Bull. Amer. Math. Soc. (NS) 11 (1984), no. 2, 347-350. 21. GG Kasparov, The operator K -functor and extensions of C