Ky Fan Theorem for Sphere Bundles

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI:10.1134/S1061920825600138

G. Panina, R. Živaljević

引用次数: 0

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

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球束的Ky范定理

经典的Ky Fan定理是Borsuk-Ulam定理的组合等价。它是塔克引理的推广和扩展，就像它的前身一样，它指出了三角球顶点对映着色\(S^n\)的重要性质。在这里，我们描述了用三角球束的总空间代替球的情形下Ky Fan定理的推广。Doi 10.1134/ s1061920825600138

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.