Commutative Geometries are Spin Manifolds
Mathematical Physics
2007-05-23 v2 Differential Geometry
Functional Analysis
math.MP
Abstract
In [1], Connes presented axioms governing noncommutative geometry. He went on to claim that when specialised to the commutative case, these axioms recover spin or spin^c geometry depending on whether the geometry is ''real'' or not. We attempt to flesh out the details of Connes' ideas. As an illustration we present a proof of his claim, partly extending the validity of the result to pseudo-Riemannian spin manifolds. Throughout we are as explicit and elementary as possible.
Cite
@article{arxiv.math-ph/9903021,
title = {Commutative Geometries are Spin Manifolds},
author = {A. Rennie},
journal= {arXiv preprint arXiv:math-ph/9903021},
year = {2007}
}
Comments
Re-tex to get references right. This is a revised version of a previously incorrect version. Changes to the central portion of proof are extensive. 48 pp