English

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 KK-theory and Lipschitz topological KK-theory, combined with an earlier vanishing theorem for the quantitative higher index.

Keywords

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

R2 v1 2026-06-24T10:28:53.628Z