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The `Holiverse': holistic eversion of the 2-sphere in $\R^3$

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arxiv 1008.0916 v1 pith:JQMWVJNV submitted 2010-08-05 math.GT math-phmath.MP

Iain R. Aitchison This is my paper · ORCID
classification math.GTmath-phmath.MP
keywords eversionspheregiveproofconceptualconnectedembeddedfibration
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abstract

We give a short, simple and conceptual proof, based on spin structures, of sphere eversion: an embedded 2-sphere in $R^3$ can be turned inside out by regular homotopy. Ingredients of this eversion are seamlessly connected. We also give the mathematical origins of the proof: the Hopf fibration, and the topological structure of real-projective 3-space.

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  1. The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow

    math.DG 2025-06 conditional novelty 8.0 of 10

    Every immersed 2-sphere with Willmore energy at most 12π admits an energy-nonincreasing regular homotopy to a round sphere or to a surface in the explicit family J, giving exactly four regular homotopy classes below 12π.

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