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arXiv · 0911.3602

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

Moulay-Tahar Benameur·James L. Heitsch
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Abstract

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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Moulay-Tahar Benameur, James L. Heitsch. 2009-11-18. The higher fixed point theorem for foliations I. Holonomy invariant currents. https://arxiv.org/abs/0911.3602

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