The higher fixed point theorem for foliations I. Holonomy invariant currents

Details The higher fixed point theorem for foliations I. Holonomy invariant currents The higher fixed point theorem for foliations I. Holonomy invariant currents

2009-11-18

arxiv.org/abs/0911.3602v2

Mathematics

K-Theory and Homology

This is an updated version of the paper submitted in November 2009. It will appear in the Journal of Functional Analysis.

Scientific paper

In this paper, we prove a higher Lefschetz formula for foliations in the presence of a closed Haefliger current. We associate with such a current an equivariant cyclic cohomology class of Connes' C*-algebra of the foliation, and compute its pairing with the localized equivariant K-theory in terms of local contributions near the fixed points. As special cases, we recover a number of classical results, and since we may use any closed Haefliger current on the foliation, we get new and very interesting formulae.

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