Chromatic congruences and Bernoulli numbers

Irakli Patchkoria

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arXiv · 2406.17705

Chromatic congruences and Bernoulli numbers

Irakli Patchkoria

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Abstract

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.

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BibTeX RIS

Irakli Patchkoria. 2024-06-25. Chromatic congruences and Bernoulli numbers. https://arxiv.org/abs/2406.17705

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