Chromatic congruences and Bernoulli numbers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910500982358016 |
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| author | Patchkoria, Irakli |
| author_facet | Patchkoria, Irakli |
| contents | For every natural number $n$ and a fixed prime $p$, we prove a new congruence for the orbifold Euler characteristic of a group. The $p$-adic limit of these congruences as $n$ tends to infinity recovers the Brown-Quillen congruence. We apply these results to mapping class groups and using the Harer-Zagier formula we obtain a family of congruences for Bernoulli numbers. We show that these congruences in particular recover classical congruences for Bernoulli numbers due to Kummer, Voronoi, Carlitz, and Cohen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chromatic congruences and Bernoulli numbers Patchkoria, Irakli Algebraic Topology Group Theory K-Theory and Homology Number Theory 55R40, 57K20, 11B68, 11M06 For every natural number $n$ and a fixed prime $p$, we prove a new congruence for the orbifold Euler characteristic of a group. The $p$-adic limit of these congruences as $n$ tends to infinity recovers the Brown-Quillen congruence. We apply these results to mapping class groups and using the Harer-Zagier formula we obtain a family of congruences for Bernoulli numbers. We show that these congruences in particular recover classical congruences for Bernoulli numbers due to Kummer, Voronoi, Carlitz, and Cohen. |
| title | Chromatic congruences and Bernoulli numbers |
| topic | Algebraic Topology Group Theory K-Theory and Homology Number Theory 55R40, 57K20, 11B68, 11M06 |
| url | https://arxiv.org/abs/2406.17705 |