Borsuk-Ulam theorems for products of spheres and Stiefel manifolds\n revisited

2019/02/03 by Yu Hin Chan, Shujian Chen, Chan, Yu Hin +5 · 2 citations
Computer Science · Mathematics · #54H25 #55M20 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1902.00935

openalex publication_date 2019/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a different and possibly more accessible proof of a general\nBorsuk--Ulam theorem for a product of spheres, originally due to Ramos. That\nis, we show the non-existence of certain (\ℤ/2)^k-equivariant maps\nfrom a product of k spheres to the unit sphere in a real\n(\ℤ/2)^k-representation of the same dimension. Our proof method\nallows us to derive Borsuk--Ulam theorems for certain equivariant maps from\nStiefel manifolds, from the corresponding results about products of spheres,\nleading to alternative proofs and extensions of some results of Fadell and\nHusseini.\n

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• Covering and labeling generalizations of the Borsuk-Ulam theorem
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