Inscribed squares of level sets of functions on the sphere

V. A. Vassiliev

Inscribed squares of level sets of functions on the sphere

Geometric Topology 2026-07-03 v1 Classical Analysis and ODEs

Authors: V. A. Vassiliev

Abstract

Every continuous function $f: S^2 \to {\mathbb R}$ takes the same value on the vertices of a square inscribed into a great circle of $S^2$ . Keywords: level set, configuration space, Stiefel--Whitney class, inscribed squares, Borsuk-Ulam type theorems

Keywords

level set configuration space Stiefel-Whitney class inscribed squares Borsuk-Ulam type theorems

Cite

@article{arxiv.2607.13052,
  title  = {Inscribed squares of level sets of functions on the sphere},
  author = {V. A. Vassiliev},
  journal= {arXiv preprint arXiv:2607.13052},
  year   = {2026}
}