Reducing the number of fixed points of some homeomorphisms on nonprime <mml:math alttext="$3$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>3</mml:mn></mml:math>-manifolds

Zhao, Xuezhi

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Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 25897, 19 pages
doi:10.1155/FPTA/2006/25897

Reducing the number of fixed points of some homeomorphisms on nonprime 3-manifolds

Xuezhi Zhao

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

Received 5 September 2004; Revised 15 March 2005; Accepted 21 July 2005

Copyright © 2006 Xuezhi Zhao. 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.

Abstract

We will consider the number of fixed points of homeomorphisms composed of finitely many slide homeomorphisms on closed oriented nonprime 3-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.