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

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.

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