Equivariant maps related to the topological Tverberg conjecture

TL;DR

This paper constructs equivariant maps for specific groups using obstruction theory, providing counterexamples related to the topological Tverberg conjecture and implications for Borsuk-Ulam properties.

Contribution

It introduces new equivariant maps for certain groups, answering a question by Ozaydin and impacting the understanding of the topological Tverberg conjecture.

Findings

Counterexamples to weaker versions of the Tverberg conjecture

Negative answers to Ozaydin's question

Implications for Borsuk-Ulam properties of cyclic and dihedral group representations

Abstract

Using equivariant obstruction theory we construct equivariant maps from certain classifying spaces to representation spheres for cyclic groups, product of elementary Abelian groups and dihedral groups. Restricting them to finite skeleta constructs equivariant maps between spaces which are related to the topological Tverberg conjecture. This answers negatively a question of \"Ozaydin posed in relation to weaker versions of the same conjecture. Further, it also has consequences for Borsuk-Ulam properties of representations of cyclic and dihedral groups.