Covering complexity, scalar curvature, and quantitative $K$-theory
K-Theory and Homology
2024-09-02 v2 Differential Geometry
Operator Algebras
Abstract
We establish a relationship between a certain notion of covering complexity of a Riemannian spin manifold and positive lower bounds on its scalar curvature. This makes use of a pairing between quantitative operator -theory and Lipschitz topological -theory, combined with an earlier vanishing theorem for the quantitative higher index.
Cite
@article{arxiv.2203.15003,
title = {Covering complexity, scalar curvature, and quantitative $K$-theory},
author = {Hao Guo and Guoliang Yu},
journal= {arXiv preprint arXiv:2203.15003},
year = {2024}
}
Comments
22 pages, updated to accepted version