Geometric non-commutative geometry
Geometric Topology
2020-02-07 v2 Differential Geometry
Abstract
In a recent paper, the authors proved that no spin foliation on a compact enlargeable manifold with Hausdorff homotopy graph admits a metric of positive scalar curvature on its leaves. This result extends groundbreaking results of Lichnerowicz, Gromov and Lawson, and Connes on the non-existence of metrics of positive scalar curvature. In this paper we review in more detail the material needed for the proof of our theorem and we extend our non-existence results to non-compact manifolds of bounded geometry. We also give a first obstruction result for the existence of metric with (not necessarily uniform) leafwise PSC in terms of the A-hat class in Haefliger cohomology.
Keywords
Cite
@article{arxiv.1909.00063,
title = {Geometric non-commutative geometry},
author = {Moulay Tahar Benameur and James L. Heitsch},
journal= {arXiv preprint arXiv:1909.00063},
year = {2020}
}