Covering complexity, scalar curvature, and quantitative $K$-theory
Hao Guo, Guoliang Yu · Pure and Applied Mathematics Quarterly · 2023
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 $K$-theory and Lipschitz topological $K$-theory, combined with an earlier vanishing theorem for the quantitative higher index.