Homology, Homotopy and Applications

Volume 19 (2017)

Number 1

Equivariant maps related to the topological Tverberg conjecture

Pages: 155 – 170

DOI: https://dx.doi.org/10.4310/HHA.2017.v19.n1.a8

Authors

Samik Basu (Department of Mathematics, Vivekananda University, Belur, Howrah, West Bengal, India)

Surojit Ghosh (Department of Mathematics, Vivekananda University, Belur, Howrah, West Bengal, India)

Abstract

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.

Keywords

Tverberg’s theorem, equivariant obstruction theory

2010 Mathematics Subject Classification

Primary 55P91. Secondary 52A35, 55S91.

Published 6 June 2017