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Stability of Homomorphisms, Coverings and Cocycles I: Equivalence

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arxiv 2310.17474 v2 pith:NXGIDTPK submitted 2023-10-26 math.GR

Michael Chapman , Alexander Lubotzky This is my paper · ORCID
classification math.GR
keywords stabilityclosecoveringshomomorphismsalmostcocyclesproblemsthree
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This paper is motivated by recent developments in group stability, high dimensional expansion, local testability of error correcting codes and topological property testing. In Part I, we formulate and motivate three stability problems: 1. Homomorphism stability: Are almost homomorphisms close to homomorphisms? 2. Covering stability: Are almost coverings of a cell complex close to genuine coverings of it? 3. Cocycle stability: Are 1-cochains whose coboundary is small close to 1-cocycles? We then prove that these three problems are equivalent.

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  1. Minimal Submanifolds and Waists of Locally Symmetric Spaces

    math.DG 2024-12 conditional novelty 8.0 of 10

    The paper proves a linear volume lower bound for codimension two minimal submanifolds of compact octonionic hyperbolic manifolds, yielding linear waists, systolic freedom, and new lattice fixed point theorems.

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