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<p>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: <i>Homomorphism stability</i>: Are almost homomorphisms close to homomorphisms? <i>Covering stability</i>: Are almost coverings of a cell complex close to genuine coverings of it? <i>Cocycle stability</i>: Are 1-cochains whose coboundary is small close to 1-cocycles? We then prove that these three problems are equivalent.</p>

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Stability of homomorphisms, coverings and cocycles I: equivalence

  • 期刊论文

  • 发表日期：

    2025年2月4日

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  • Michael Chapman,
  • Alexander Lubotzky

摘要

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: Homomorphism stability: Are almost homomorphisms close to homomorphisms? Covering stability: Are almost coverings of a cell complex close to genuine coverings of it? Cocycle stability: Are 1-cochains whose coboundary is small close to 1-cocycles? We then prove that these three problems are equivalent.