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

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

2010-08-05

arxiv.org/abs/1008.0916v1

Mathematics

Geometric Topology

16 pages; 15 figures (34 pdf files). A (crude) Povray animation of essential features of the `holiverse' will soon be posted o

Scientific paper

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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