Loeh, Clara and Witzig, Johannes (2024) Universal Finite Functorial Semi-norms. APPLIED CATEGORICAL STRUCTURES, 32 (4): 19. ISSN 0927-2852, 1572-9095
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Functorial semi-norms on singular homology measure the "size" of homology classes. A geometrically meaningful example is the & ell;1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell <^>1$$\end{document}-semi-norm. However, the & ell;1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell <^>1$$\end{document}-semi-norm is not universal in the sense that it does not vanish on as few classes as possible. We show that universal finite functorial semi-norms do exist on singular homology on the category of topological spaces that are homotopy equivalent to finite CW-complexes. Our arguments also apply to more general settings of functorial semi-norms.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | VOLUME; HOMOLOGY; Functorial semi-norms; Universality; Singular homology; Simplicial volume |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Clara Löh |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Jul 2025 12:24 |
| Last Modified: | 15 Jul 2025 12:24 |
| URI: | https://pred.uni-regensburg.de/id/eprint/63471 |
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