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Riemannian manifolds in noncommutative geometry

Lord, Steven; Rennie, Adam; Varilly, Joseph

Description

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
URI: http://hdl.handle.net/1885/62155
Source: Journal of Geometry and Physics
DOI: 10.1016/j.geomphys.2012.03.004

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