English

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

Geometric Topology 2010-08-06 v1 Mathematical Physics math.MP

Abstract

We give a short, simple and conceptual proof, based on spin structures, of sphere eversion: an embedded 2-sphere in R3R^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.

Keywords

Cite

@article{arxiv.1008.0916,
  title  = {The `Holiverse': holistic eversion of the 2-sphere in $\R^3$},
  author = {Iain R. Aitchison},
  journal= {arXiv preprint arXiv:1008.0916},
  year   = {2010}
}

Comments

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