Riemannian manifolds in noncommutative geometry
-
Altmetric Citations
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.
Collections | ANU 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 |
Download
File | Description | Size | Format | Image |
---|---|---|---|---|
01_Lord_Riemannian_manifolds_in_2012.pdf | 429.66 kB | Adobe PDF | Request a copy |
Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.
Updated: 17 November 2022/ Responsible Officer: University Librarian/ Page Contact: Library Systems & Web Coordinator