Vol. 5, No. 2, 2020

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The Godbillon–Vey invariant and equivariant $KK$-theory

Lachlan MacDonald and Adam Rennie

Vol. 5 (2020), No. 2, 249–294
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.

Keywords
foliation, Godbillon–Vey, bivariant $K$-theory, equivariant, spectral triple
Mathematical Subject Classification 2010
Primary: 19K35
Milestones
Received: 23 November 2018
Revised: 21 October 2019
Accepted: 13 November 2019
Published: 20 June 2020
Authors
Lachlan MacDonald
School of Mathematics and Applied Statistics
University of Wollongong
Wollongong, NSW
Australia
Adam Rennie
School of Mathematics and Applied Statistics
University of Wollongong
Wollongong, NSW
Australia