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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A higher Lefschetz formula for flat bundles


Author: Moulay-Tahar Benameur
Journal: Trans. Amer. Math. Soc. 355 (2003), 119-142
MSC (2000): Primary 19L47, 19M05, 19K56
DOI: https://doi.org/10.1090/S0002-9947-02-03111-2
Published electronically: September 5, 2002
MathSciNet review: 1928080
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Abstract: In this paper, we prove a fixed point formula for flat bundles. To this end, we use cyclic cocycles which are constructed out of closed invariant currents. We show that such cyclic cocycles are equivariant with respect to isometric longitudinal actions of compact Lie groups. This enables us to prove fixed point formulae in the cyclic homology of the smooth convolution algebra of the foliation.


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Additional Information

Moulay-Tahar Benameur
Affiliation: Institut Girard Desargues, Université Claude Bernard, Lyon 1, France
Email: benameur@igd.univ-lyon1.fr

DOI: https://doi.org/10.1090/S0002-9947-02-03111-2
Keywords: $C^*$-algebra, $K$-theory, Lefschetz, foliations.
Received by editor(s): November 23, 2001
Received by editor(s) in revised form: March 12, 2002
Published electronically: September 5, 2002
Article copyright: © Copyright 2002 American Mathematical Society