Skip navigation
Skip navigation

Riemannian manifolds in noncommutative geometry

Lord, Steven; Rennie, Adam; Varilly, Joseph


We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin. c manifolds; and conversely, in the presence of a spin. c structure. We also show how to obtain an analogue of Kasparov's fundamental class for a Riemannian manifold, and the associated notion of Poincaré duality. Along the way we clarify the bimodule and first-order conditions for spectral triples.

CollectionsANU Research Publications
Date published: 2012
Type: Journal article
Source: Journal of Geometry and Physics
DOI: 10.1016/j.geomphys.2012.03.004


File Description SizeFormat Image
01_Lord_Riemannian_manifolds_in_2012.pdf429.66 kBAdobe PDF    Request a copy

Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  23 August 2018/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator