SO(3): The Principal Bundle Structure

Ján Brajerčík () and Demeter Krupka
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Ján Brajerčík: Department of Physics, Mathematics and Technologies, Faculty of Humanities and Natural Sciences, University of Prešov, 17. Novembra 1, 08001 Prešov, Slovakia
Demeter Krupka: Lepage Research Institute, 17. Novembra 1, 08001 Prešov, Slovakia

Mathematics, 2025, vol. 13, issue 7, 1-23

Abstract: In this article, the special orthogonal group SO(3) is considered as a topological group. We show that SO(3) has the structure of a principal SO(2)-bundle over the sphere S 2 . As a consequence, we prove that every orbit of an SO(3)-action on a topological space is either trivial or homeomorphic to S 2 . We also introduce a topological atlas on SO(3), by means of its principal bundle structure, and prove that this atlas is smooth.

Keywords: special orthogonal matrix; group action; orbit; principal bundle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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