© Xuezhi Zhao. 2006
Received: 5 September 2004
Accepted: 21 July 2005
Published: 1 March 2006
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.
- Brown RF: The Lefschetz Fixed Point Theorem. Scott, Foresman, Illinois; 1971.MATHGoogle Scholar
- Fried D: Homological identities for closed orbits. Inventiones Mathematicae 1983,71(2):419–442. 10.1007/BF01389105MathSciNetView ArticleMATHGoogle Scholar
- Ghrist RW, Holmes PJ, Sullivan MC: Knots and Links in Three-Dimensional Flows, Lecture Notes in Mathematics. Volume 1654. Springer, Berlin; 1997.MATHGoogle Scholar
- Jiang BJ: Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics. Volume 14. American Mathematical Society, Rhode Island; 1983.View ArticleGoogle Scholar
- Jiang BJ, Guo JH: Fixed points of surface diffeomorphisms. Pacific Journal of Mathematics 1993,160(1):67–89.MathSciNetView ArticleMATHGoogle Scholar
- 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
- 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
- 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
- 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
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