Equivariant Nielsen root theory for G-maps

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.