NIELSEN THEORY ON INFRA-NILMANIFOLDS MODELED ON THE GROUP OF UNI-TRIANGULAR MATRICES

摘要

Let Nil(m) be the group of mxm uni-triangular matrices. Then it is a connected and simply connected (m - 1)-step nilpotent Lie group. Using the averaging formulas, we compute the spectra of the Lefschetz, Nielsen and Reidemeister (coincidence) numbers of maps on infra-nilmanifolds modeled on Nil(m). As a byproduct, we prove that the Bieberbach groups of Nil(m) (m >= 4) with as its nil-radical satisfy the R-infinity property.