Classification of the topological holonomy groups in $SO(3)$

Naoya Ando

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arXiv · 2507.20593

Classification of the topological holonomy groups in $SO(3)$

Naoya Ando

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Abstract

In this paper, we obtain classification of the topological holonomy groups in $SO(3)$. Such a group is given by one of the following: a finite group (such groups are classified by Klein); a commutative infinite group which is generated by one or two elements, and dense in a subgroup of $SO(3)$ isomorphic to $SO(2)$; a non-commutative infinite group generated by two elements of order $2$, $\infty$ such that these rotation axes are orthogonal; a non-commutative infinite group which is dense in $SO(3)$.

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Naoya Ando. 2025-07-28. Classification of the topological holonomy groups in $SO(3)$. https://arxiv.org/abs/2507.20593

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