Chromatic spherical invariant and Hennings invariant of 3-dimensional manifolds

Julie Reina

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arXiv · 2507.06019

Chromatic spherical invariant and Hennings invariant of 3-dimensional manifolds

Julie Reina

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Abstract

This paper establishes a relation between two invariants of $3$-dimensional manifolds: the chromatic spherical invariant $\mathcal{K}$ and the Hennings-Kauffman-Radford invariant $\operatorname{HKR}$. We show that, for a spherical Hopf algebra $H$, the invariant $\mathcal{K}$ associated to the pivotal category of finite-dimensional $H$-modules is equal to the invariant $\operatorname{HKR}$ associated to the Drinfeld double $D(H)$ of the same Hopf algebra.

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Julie Reina. 2025-07-08. Chromatic spherical invariant and Hennings invariant of 3-dimensional manifolds. https://arxiv.org/abs/2507.06019

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