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Pure and Applied Mathematics Quarterly
Volume 19 (2023)
Number 6
Special Issue in honor of Professor Blaine Lawson’s 80th birthday
Guest Editors: Shiu-Yuen Cheng, Paulo Lima-Filho, and Stephen Shing-Toung Yau
Covering complexity, scalar curvature, and quantitative $K$-theory
Pages: 2951 – 2972
DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n6.a13
Authors
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.
The second author is partially supported by NSF grants 1700021 and 2000082, and by the Simons Fellows Program.
Received 28 March 2022
Received revised 25 December 2022
Accepted 12 February 2023
Published 30 January 2024