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

Yu Hin Chan, Shujian Chen, Florian Frick, J. Tristan Hull

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.

Keywords


Borsuk-Ulam theorem; Stiefel manifold; equivariant map

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