Abstract Excision and $\ell^1$-Homology
| Autor: | Witzig, Johannes |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | We use the abstract setting of excisive functors in the language of $\infty$-categories to show that the best approximation to the $\ell^1$-homology functor by an excisive functor is trivial. Then we make an effort to explain the used language on a conceptual level for those who do not feel at home with $\infty$-categories, prove that the singular chain complex functor is indeed excisive in the abstract sense, and show how the latter leads to classical excision statements in the form of Mayer-Vietoris sequences. Comment: 35 pages; v2: revised version, including: comments on related results (Introduction), more explicit handling of "size" (Introduction, Remarks 2.3, 2.4, 2.11), removal of claim about homology from Theorem 1.7, further explanatory material (Outlook 2.24, Section 2.4); to appear in Confluentes Mathematici |
| Databáze: | arXiv |
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