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arXiv · 1902.00935

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

Yu Hin Chan·Shujian Chen·Florian Frick·J. Tristan Hull
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Abstract

We give a different and possibly more accessible proof of a general Borsuk--Ulam theorem for a product of spheres, originally due to Ramos. That is, we show the non-existence of certain $(\mathbb{Z}/2)^k$-equivariant maps from a product of $k$ spheres to the unit sphere in a real $(\mathbb{Z}/2)^k$-representation of the same dimension. Our proof method allows us to derive Borsuk--Ulam theorems for certain equivariant maps from Stiefel manifolds, from the corresponding results about products of spheres, leading to alternative proofs and extensions of some results of Fadell and Husseini.

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Yu Hin Chan, Shujian Chen, Florian Frick, J. Tristan Hull. 2019-02-03. Borsuk-Ulam theorems for products of spheres and Stiefel manifolds revisited. https://arxiv.org/abs/1902.00935

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