Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 6, pp 1855–1869 | Cite as

Self-homeomorphisms and Degree \(\pm \,1\) Self-maps on Lens Spaces

  • Xiaotian Pan
  • Bingzhe HouEmail author
  • Zhongyang Zhang
Original Paper


In this article, we give a sufficient and necessary condition to that a degree \(\pm \,1\) self-map on a \((2n-1)\)-dimensional lens space for \(n \ge 2\) 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 \(S^{2n-1}\) is obtained.


Lens spaces Self-homeomorphisms Fundamental groups Endomorphisms Topological conjugacies 

Mathematics Subject Classification

20F34 55M25 57N99 37C15 



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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.School of MathematicsJilin UniversityChangchunPeople’s Republic of China
  2. 2.Department of Basic ScienceAviation University Air ForceChangchunPeople’s Republic of China

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