The Godbillon-Vey invariant in equivariant $KK$-theory

Abstract

We construct a groupoid equivariant Kasparov class for transversely oriented foliations in all codimensions. In codimension 1 we show that the Chern character of an associated semifinite spectral triple recovers the Connes-Moscovici cyclic cocycle for the Godbillon-Vey secondary characteristic class.

References in corpus (6)

• Hopf algebras, cyclic cohomology and the transverse index theory
• KMS states of quasi-free dynamics on Pimsner algebras
• A local global principle for regular operators in Hilbert C*-modules
• Characters of Cycles, Equivariant Characteristic Classes and Fredholm Modules
• Transverse noncommutative geometry of foliations
• A Baum-Connes conjecture for singular foliations

Cited by in corpus (3)

• The Holonomy Groupoids of Singularly Foliated Bundles
• Equivariant $KK$-theory for non-Hausdorff groupoids
• Transversals, duality, and irrational rotation