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

Lachlan MacDonald; Adam Rennie

doi:10.2140/akt.2020.5.249

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.

Citation

Download Citation

Lachlan MacDonald. Adam Rennie. "The Godbillon–Vey invariant and equivariant $KK$-theory." Ann. K-Theory 5 (2) 249 - 294, 2020. https://doi.org/10.2140/akt.2020.5.249

Information

Received: 23 November 2018; Revised: 21 October 2019; Accepted: 13 November 2019; Published: 2020

First available in Project Euclid: 11 August 2020

zbMATH: 07224514

MathSciNet: MR4113770

Digital Object Identifier: 10.2140/akt.2020.5.249

Subjects:

Primary: 19K35

Keywords: bivariant $K$-theory , equivariant , Foliation , Godbillon–Vey , spectral triple

Abstract

Citation

Information

KEYWORDS/PHRASES

PUBLICATION TITLE:

PUBLICATION YEARS