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Abstract <p> The classical Ky Fan theorem is a combinatorial equivalent of the Borsuk–Ulam theorem. It is a generalization and extension of Tucker’s lemma and, just like its predecessor, it pinpoints important properties of antipodal colorings of vertices of a triangulated sphere <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3220_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(S^n\)</EquationSource> </InlineEquation>. Here we describe generalizations of Ky Fan theorem for the case when the sphere is replaced by the total space of a triangulated sphere bundle. </p> <p> <b> DOI</b> 10.1134/S1061920825600138 </p>

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Ky Fan Theorem for Sphere Bundles

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • G. Panina,
  • R. Živaljević

摘要

Abstract

The classical Ky Fan theorem is a combinatorial equivalent of the Borsuk–Ulam theorem. It is a generalization and extension of Tucker’s lemma and, just like its predecessor, it pinpoints important properties of antipodal colorings of vertices of a triangulated sphere \(S^n\) . Here we describe generalizations of Ky Fan theorem for the case when the sphere is replaced by the total space of a triangulated sphere bundle.

DOI 10.1134/S1061920825600138