2009/11/18 by Moulay-Tahar Benameur, Benameur, Moulay-Tahar, James L. Heitsch +1
Mathematics · #19K56 #19L47 #19M05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:19K56 #msc:19L47 #msc:19M05
paper · pdf · doi:10.48550/arxiv.0911.3602
This is an updated version of the paper submitted in November 2009. It will appear in the Journal of Functional Analysis.
openalex publication_date 2009/11/18 · arxiv created 2010/03/31 · arxiv updated 2010/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.