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Fixed point sets of maps homotopic to a given map


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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Correspondence to Christina L Soderlund.

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Soderlund, C.L. Fixed point sets of maps homotopic to a given map. Fixed Point Theory Appl 2006, 46052 (2006).

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  • Differential Geometry
  • Computational Biology