Determination of compact Lie groups with the Borsuk-Ulam property

2021/07/28 by Nagasaki, Ikumitsu
#55M20 #55S35 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.13158

Abstract

In this paper, we shall discuss the classical question of which compact Lie groups have the Borsuk-Ulam property and in particular we shall show that every extension group of a n-torus by a cyclic group of prime order does not have the Borsuk-Ulam property. This leads us that the only compact Lie groups with the Borsuk-Ulam property are an elementary abelian p-group and an n-torus, which is a final answer to the question.

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