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Fixed point sets of maps homotopic to a given map

Fixed Point Theory and Applications volume 2006, Article number: 46052 (2006) Cite this article

Abstract

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.

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

    Christina L Soderlund

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  1. Christina L Soderlund
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Correspondence to Christina L Soderlund.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Soderlund, C.L. Fixed point sets of maps homotopic to a given map. Fixed Point Theory Appl 2006, 46052 (2006). https://doi.org/10.1155/FPTA/2006/46052

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  • DOI: https://doi.org/10.1155/FPTA/2006/46052

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