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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.12971 |
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| _version_ | 1866929406746820608 |
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| author | Loeh, Clara Witzig, Johannes |
| author_facet | Loeh, Clara Witzig, Johannes |
| contents | Functorial semi-norms on singular homology measure the "size" of homology classes. A geometrically meaningful example is the $\ell^1$-semi-norm. However, the $\ell^1$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_12971 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Universal finite functorial semi-norms Loeh, Clara Witzig, Johannes Category Theory Algebraic Topology Functorial semi-norms on singular homology measure the "size" of homology classes. A geometrically meaningful example is the $\ell^1$-semi-norm. However, the $\ell^1$-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. |
| title | Universal finite functorial semi-norms |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2209.12971 |