Inscribed squares of level sets of functions on the sphere

2026/07/03 by V. A. Vassiliev
Mathematics · #math.GT #math.CA

paper · pdf

Abstract

According to a theorem by F.~Dyson, every continuous function f: S² → \mathbb R takes the same value at the vertices of a square inscribed into a great circle of S². We give a proof of this statement based on the theory of characteristic classes and indicate other potential applications of this approach.

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