Least number of periodic points of self-maps of Lie groups (Q741225)

In this work the author studies the following problem. We are given a self map of a Lie group \(f:X\to X\), an integer \(k\) and we ask if \(f\) is homotopic to a smooth map \(h\) realizing the least number of \(k\)-periodic points? In the case where \(X\) is a simply-connected DJ-manifold the author gives a necessary and sufficient condition for the existence of such smooth map \(h\) with a single \(k\)-periodic point. This is Theorem \(4.1\). For the case non-simply connected the author generalizes Theorem \(4.1\) to all compact connected DJ-manifolds with free fundamental groups. This is Theorem \(9.3\). (Where a manifold \(M\) is called a DJ-manifold if it is (i) an exterior rational space (ii) a Jiang space (iii) \(\pi_1(M)\) is a free abelian group).