A simple eversion of the 2-sphere with a unique quadruple point
Denis Sauvaget (LAGA)
TL;DR
This paper presents a straightforward example of turning a 2-sphere inside out in three-dimensional space, featuring a single quadruple point, achieved without using homotopical methods, inspired by Morse theory.
Contribution
It provides a novel, simple eversion of the 2-sphere with a unique quadruple point, avoiding traditional homotopical techniques.
Findings
Constructed an explicit eversion with one quadruple point
Demonstrated the eversion without homotopical tools
Inspired by Morse theory methods
Abstract
We give an example of an eversion of the 2-sphere in the Euclidean 3-space, inspired by Morse theory, with a unique quadruple point. No homotopical tool is used.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · Homotopy and Cohomology in Algebraic Topology