𝐺-coincidences for maps of homotopy spheres into CW-complexes

Abstract

Let G G be a finite group acting freely in a CW-complex Σ m \Sigma ^{m} which is a homotopy m m -dimensional sphere and let f : Σ m → Y f:\Sigma ^{m} \to Y be a map of Σ m \Sigma ^{m} to a finite k k -dimensional CW-complex Y Y . We show that if m ≥ | G | k m\geq \vert G\vert k , then f f has an ( H , G ) (H,G) -coincidence for some nontrivial subgroup H H of G G .