Nielsen theory on nilmanifolds of the standard filiform lie group

Abstract

Let M be a nilmanifold modeled on the standard filiform Lie group H m+1 and let f: M→ M be a self-map. Using the averaging formulas, we compute the spectra of the Lefschetz, Nielsen, and Reidemeister (coincidence) numbers of maps f on M. Moreover, we give explicit formulas for a complete computation of the Nielsen type numbers NP n (f) and NΦn(f). We also give a complete description of the sets of homotopy minimal periods of all such maps on M.