Self-homeomorphisms and Degree ±1 Self-maps on Lens Spaces.

In this article, we give a sufficient and necessary condition to that a degree ± 1 self-map on a (2 n - 1) -dimensional lens space for n ≥ 2 is homotopic to a self-homeomorphism. In fact, we show how the endomorphism induced by a homeomorphism can act on the fundamental group of the lens space. Moreover, we provide a specific description of a class of lens spaces which admit self-homeomorphisms inducing nontrivial automorphisms on the fundamental groups. Furthermore, the topologically conjugate classification for a special class of periodic homeomorphisms on S 2 n - 1 is obtained. [ABSTRACT FROM AUTHOR]