Stability of Homomorphisms, Coverings and Cocycles I: Equivalence
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929299424018432 |
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| author | Chapman, Michael Lubotzky, Alexander |
| author_facet | Chapman, Michael Lubotzky, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17474 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability of Homomorphisms, Coverings and Cocycles I: Equivalence Chapman, Michael Lubotzky, Alexander Group Theory 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. |
| title | Stability of Homomorphisms, Coverings and Cocycles I: Equivalence |
| topic | Group Theory |
| url | https://arxiv.org/abs/2310.17474 |