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  • Research Article
  • Open Access

Reducing the number of fixed points of some homeomorphisms on nonprime -manifolds

Fixed Point Theory and Applications20062006:25897

  • Received: 5 September 2004
  • Accepted: 21 July 2005
  • Published:


We will consider the number of fixed points of homeomorphisms composed of finitely many slide homeomorphisms on closed oriented nonprime -manifolds. By isotoping such homeomorphisms, we try to reduce their fixed point numbers. The numbers obtained are determined by the intersection information of sliding spheres and sliding paths of the slide homeomorphisms involved.


  • Differential Geometry
  • Computational Biology


Authors’ Affiliations

Department of Mathematics, Capital Normal University, Beijing, 100037, China


  1. Brown RF: The Lefschetz Fixed Point Theorem. Scott, Foresman, Illinois; 1971.MATHGoogle Scholar
  2. Fried D: Homological identities for closed orbits. Inventiones Mathematicae 1983,71(2):419–442. 10.1007/BF01389105MathSciNetView ArticleMATHGoogle Scholar
  3. Ghrist RW, Holmes PJ, Sullivan MC: Knots and Links in Three-Dimensional Flows, Lecture Notes in Mathematics. Volume 1654. Springer, Berlin; 1997.MATHGoogle Scholar
  4. Jiang BJ: Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics. Volume 14. American Mathematical Society, Rhode Island; 1983.View ArticleGoogle Scholar
  5. Jiang BJ, Guo JH: Fixed points of surface diffeomorphisms. Pacific Journal of Mathematics 1993,160(1):67–89.MathSciNetView ArticleMATHGoogle Scholar
  6. Jiang BJ, Wang S, Wu Y-Q: Homeomorphisms of 3-manifolds and the realization of Nielsen number. Communications in Analysis and Geometry 2001,9(4):825–877.MathSciNetView ArticleMATHGoogle Scholar
  7. Kelly MR: The Nielsen number as an isotopy invariant. Topology and its Applications 1995,62(2):127–143. 10.1016/0166-8641(94)00053-6MathSciNetView ArticleMATHGoogle Scholar
  8. McCullough D: Mappings of reducible 3-manifolds. In Geometric and Algebraic Topology, Banach Center Publ.. Volume 18. PWN—Polish Scientific, Warsaw; 1986:61–76.Google Scholar
  9. Zhao X: On the Nielsen numbers of slide homeomorphisms on 3-manifolds. Topology and its Applications 2004,136(1–3):169–188. 10.1016/S0166-8641(03)00218-9MathSciNetView ArticleMATHGoogle Scholar


© Xuezhi Zhao. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.