On extending results of Gluck and Warner on fibrations of spheres by great subspheres

Eric Yu

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arXiv · 2605.06712

On extending results of Gluck and Warner on fibrations of spheres by great subspheres

Eric Yu

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Abstract

In this paper, we build upon the work of Gluck and Warner who showed in 1983 that the set of positively oriented fibrations of a 3-sphere by oriented great circles is in bijection with the set of distance-decreasing maps from the 2-sphere to itself. One approach to generalizing their result to higher-dimensional spheres involves understanding when exactly two Hopf fibrations of $S^{2n-1}$ are guaranteed to agree on a fiber. We give a complete characterization of this phenomenon, and we discuss the barriers which prevent us from obtaining a fully general version of Gluck and Warner's result.

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Eric Yu. 2026-05-06. On extending results of Gluck and Warner on fibrations of spheres by great subspheres. https://arxiv.org/abs/2605.06712

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