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  • Research Article
  • Open Access

Epsilon Nielsen fixed point theory

Fixed Point Theory and Applications20062006:29470

  • Received: 11 October 2004
  • Accepted: 21 July 2005
  • Published:


Let be a map of a compact, connected Riemannian manifold, with or without boundary. For sufficiently small, we introduce an -Nielsen number that is a lower bound for the number of fixed points of all self-maps of that are -homotopic to . We prove that there is always a map that is -homotopic to such that has exactly fixed points. We describe procedures for calculating for maps of -manifolds.


  • Differential Geometry
  • Point Theory
  • Computational Biology
  • Fixed Point Theory
  • Nielsen Fixed Point Theory


Authors’ Affiliations

Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA


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© Robert F. Brown. 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.