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arXiv · 2508.19214

Duality for arithmetic Dijkgraaf-Witten theory

Jaro Eichler
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Abstract

Naidu classified pairs of finite groups and 3-cocycles that lead to equivalent Dijkgraaf-Witten theories for 3-manifolds. We establish analogous equivalences for arithmetic Dijkgraaf-Witten theory over totally imaginary number fields F containing n-th roots of unity, where n is invertible on X subset spec O_F. For the full ring of integers X = spec O_F, we give examples with quadratic fields and the quaternion group Q_8 where these equivalences fail, but also identify sufficient conditions under which they still hold.

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Jaro Eichler. 2025-08-26. Duality for arithmetic Dijkgraaf-Witten theory. https://arxiv.org/abs/2508.19214

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