Homology, Homotopy and Applications
Volume 19 (2017)
Equivariant maps related to the topological Tverberg conjecture
Pages: 155 – 170
Using equivariant obstruction theory we construct equivariant maps from certain universal spaces to representation spheres for cyclic groups, products 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 Özaydin 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.
Tverberg’s theorem, equivariant obstruction theory
2010 Mathematics Subject Classification
Primary 55P91. Secondary 52A35, 55S91.