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

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.

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