Geodesic
Abstract Excision and ℓ 1 -Homology
Witzig, Johannes1
1 Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
Confluentes Mathematici, Tome 15 (2023), pp. 107-136

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We use the abstract setting of excisive functors in the language of ∞-categories to show that the best approximation to the ℓ 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 ∞-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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DOI : 10.5802/cml.95
Classification : 55N35, 55U35, 18F50, 18N60
Keywords: $\ell ^1$-homology, excision, excisive approximation, $\infty $-categories

Witzig, Johannes 1

1 Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
Licence : CC-BY-NC-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Witzig, Johannes. Abstract Excision and $\ell ^1$-Homology. Confluentes Mathematici, Tome 15 (2023), pp. 107-136. doi: 10.5802/cml.95

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