The existence of S¹× C_p-maps between representation spheres and its applications

2024/10/10 by Nagasaki, Ikumitsu
#55M25 #55S91 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.07570

Abstract

We show the existence of S¹× C_p-maps between certain representation spheres. As an application, we show that, in the family of abelian compact Lie groups, a group G has the weak Borsuk-Ulam property (in the sense of Bartsch) if and only if G is either a finite abelian p-group or a k-torus.

Related

• Bourgin-Yang versions of the Borsuk-Ulam theorem for p-toral groups
• Borsuk--Ulam theorems for elementary abelian 2-groups
• Determination of compact Lie groups with the Borsuk-Ulam property
• Equivariant maps related to the topological Tverberg conjecture
• Maps between spherical group rings