On genus theory for 3-manifolds in arithmetic topology
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913906409078784 |
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| author | Tashiro, Hirotaka |
| author_facet | Tashiro, Hirotaka |
| contents | Based on the analogies of arithmetic topology, we show a topological analogue of Hilbert's Satz 90 for idele groups and utilize our previously established Hasse norm principle to present a proof of an Iyanaga--Tamagawa type genus formula for finite abelian branched covers over integral homology 3-spheres in a very parallel manner to the case of number theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On genus theory for 3-manifolds in arithmetic topology Tashiro, Hirotaka Geometric Topology Number Theory 57M12, 11R37 Based on the analogies of arithmetic topology, we show a topological analogue of Hilbert's Satz 90 for idele groups and utilize our previously established Hasse norm principle to present a proof of an Iyanaga--Tamagawa type genus formula for finite abelian branched covers over integral homology 3-spheres in a very parallel manner to the case of number theory. |
| title | On genus theory for 3-manifolds in arithmetic topology |
| topic | Geometric Topology Number Theory 57M12, 11R37 |
| url | https://arxiv.org/abs/2505.17486 |