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Comparison of secondary invariants of algebraic K-theory

Published online by Cambridge University Press:  21 July 2010

J. Kaad
J. Kaad
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark, [email protected]
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Abstract

In the context of 2-summable Fredholm modules, we prove that the Connes-Karoubi multiplicative character coincides with Brown's determinant invariant on algebraic K-theory.

Keywords

Algebraic K2Fredholm determinantMultiplicative character
Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 1 , August 2011 , pp. 169 - 182
Copyright
Copyright © ISOPP 2010

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References

1.Brown, L. G., The Determinant Invariant for Operators with Trace Class Self Commutators, Proc. Conf. on Operator Theory, Lecture Notes in Math. 345, Springer-Verlag, Berlin, Heidelberg, and New York, 1973, 210–228.CrossRefGoogle Scholar
2.Brown, L. G., Operator Algebras and Algebraic K.theory, Bull. Amer. Math. Soc., 81, 1973, 1119–1121.Google Scholar
3.Carey, R. W., Pincus, J. D.. Perturbation Vectors, Integral Equations Operator Theory 35, 1999, 271–365.CrossRefGoogle Scholar
4.Carey, R. W., Pincus, J. D.. Steinberg Symbols Modulo the Trace Class, Holonomy, and Limit Theorems for Toeplitz Determinants, Transactions of the American Mathematical Society 358, 2004, 509–551.CrossRefGoogle Scholar
5.Connes, A. and Karoubi, M., Caractère multiplicatif d'un module de Fredholm, K-theory 2, 1988, 431–463.CrossRefGoogle Scholar
6.Helton, J. W. and Howe, R. E., Integral Operators: Commutators, Traces, Index, and Homology, Proc. Conf. on Operator Theory, Lecture Notes in Math. 345, Springer-Verlag, Berlin, Heidelberg, New York, 1973, 141–209.Google Scholar
7.Kaad, J., A calculation of the multiplicative character, to appear in Journal of Noncommutative Geometry.Google Scholar
8.Karoubi, M., Homologie Cyclique et K-théorie, Astérisque 149, 1987.Google Scholar
9.Milnor, J., Introduction to Algebraic K-theory, Annals of Math. Studies 72, Princeton Univ. Press, Princeton, 1971.Google Scholar
10.Macduff, D. and de la Harpe, P., Acyclic groups of automorphisms, Comment. Math. Helv. 58, 1983, 48–71.Google Scholar
11.Rosenberg, J., Algebraic K-theory and Its Applications, Graduate Texts in Math. 147, Springer-Verlag, New York, Berlin, Heidelberg, 1994.Google Scholar
12.Rosenberg, J., Comparison Between Algebraic and Topological K-Theory for Banach Algebras and C*-Algebras, Handbook of Algebraic K-theory, Springer, 2004, 843–874.Google Scholar
13.Presley, A. and Segal, G., Loop Groups, Clarendon Press, Oxford, 1986.Google Scholar
14.Wagoner, J. B., Delooping Classifying Spaces in Algebraic K-theory, Topology 11, 1972, 349–370.Google Scholar