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  • Research Article
  • Open Access

Fixed point sets of maps homotopic to a given map

Fixed Point Theory and Applications20062006:46052

  • Received: 3 December 2004
  • Accepted: 24 July 2005
  • Published:


Let be a self-map of a compact, connected polyhedron and a closed subset. We examine necessary and sufficient conditions for realizing as the fixed point set of a map homotopic to . For the case where is a subpolyhedron, two necessary conditions were presented by Schirmer in 1990 and were proven sufficient under appropriate additional hypotheses. We will show that the same conditions remain sufficient when is only assumed to be a locally contractible subset of . The relative form of the realization problem has also been solved for a subpolyhedron of . We also extend these results to the case where is a locally contractible subset.


  • Differential Geometry
  • Computational Biology


Authors’ Affiliations

Department of Mathematics, California Lutheran University, 60 West Olsen Road 3750, Thousand Oaks, CA 91360-2700, USA


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© Christina L. Soderlund. 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.