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arXiv · 2203.15003

Covering complexity, scalar curvature, and quantitative $K$-theory

Hao Guo·Guoliang Yu
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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 $K$-theory and Lipschitz topological $K$-theory, combined with an earlier vanishing theorem for the quantitative higher index.

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BibTeXRIS

Hao Guo, Guoliang Yu. 2022-03-28. Covering complexity, scalar curvature, and quantitative $K$-theory. https://doi.org/10.4310/pamq.2023.v19.n6.a13

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