The `Holiverse': holistic eversion of the 2-sphere in \R³

2010/08/05 by Iain R. Aitchison, Aitchison, Iain R. · 1 citation
Mathematics · Physics and Astronomy · #00A66 (Secondary) #57R42 (Primary) 57M60 #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Mathematical Physics (math-ph) #Mathematics and Applications #math-ph #math.GT #math.MP #msc:00A66 #msc:57M60 #msc:57R42

paper · pdf · doi:10.48550/arxiv.1008.0916

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

arxiv created 2010/08/05 · openalex publication_date 2010/08/05 · arxiv updated 2010/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a short, simple and conceptual proof, based on spin structures, of sphere eversion: an embedded 2-sphere in R³ 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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