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

Iain R. Aitchison

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arXiv · 1008.0916

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

Iain R. Aitchison

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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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Iain R. Aitchison. 2010-08-05. The `Holiverse': holistic eversion of the 2-sphere in $\R^3$. https://arxiv.org/abs/1008.0916

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