Twisted burnside theorem for two-step torsion-free nilpotent groups

Abstract

It is proved that the Reidemeister number of any automorphism of any finitely generated torsion-free two-step nilpotent group coincides with the number of fixed points of the corresponding homeomorphism of the finitedimensional part of the dual space (of equivalence classes of unitary representations) provided that at least one of these numbers is finite. An important example of the discrete Heisenberg group is studied in detail.