Abstract Excision and $\ell^1$-Homology

Johannes Witzig

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arXiv · 2203.06120

Abstract Excision and $\ell^1$-Homology

Johannes Witzig

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Abstract

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.

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Johannes Witzig. 2022-03-11. Abstract Excision and $\ell^1$-Homology. https://arxiv.org/abs/2203.06120

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