Equivariant Nielsen root theory for G-maps

Abstract

Let X be a compact Hausdorff space, Y be a connected topological manifold, f : X → Y be a map between closed manifolds and a ∈ Y . The vanishing of the Nielsen root number N ( f ; a ) implies that f is homotopic to a root free map h, i.e., h ∼ f and h − 1 ( a ) = ∅ . In this paper, we prove an equivariant analog of this result for G-maps between G-spaces where G is a finite group.