Computation of the local generalized H-Lefschetz number

Let X be a connected, locally finite polyhedron. For U a compact, connected subpolyhedron of X, let f: U → X be a map with Fix(f) ∩ ∂U = Ø. The local H-Nielsen number N(f) is a lower bound for the number of fixed points of any map in a restricted homotopy class of f. We prove that the local generalized H-Lefschetz number LH(f; f̃, \̃gi) can, in certain cases, be expressed in terms of the isotropy subgroups of the local Reidemeister action and the local Lefschetz numbers of the lifts of f. From LH(f; f̃, \̃gi) we determine N(f). We consider applications to lens spaces and to a spherical space form.