Conformal Structures in Noncommutative Geometry
Differential Geometry
2011-11-09 v3
Abstract
It is well-known that a compact Riemannian spin manifold can be reconstructed from its canonical spectral triple which consists of the algebra of smooth functions, the Hilbert space of square integrable spinors and the Dirac operator. It seems to be a folklore fact that the metric can be reconstructed up to conformal equivalence if one replaces the Dirac operator D by sign(D). We give a precise formulation and proof of this fact.
Cite
@article{arxiv.0704.2119,
title = {Conformal Structures in Noncommutative Geometry},
author = {Christian Baer},
journal= {arXiv preprint arXiv:0704.2119},
year = {2011}
}