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Estimation of the number of fixed points of map extensions

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Abstract

Letf:(X,A)→(X,A) be an extension of a given map ψ:A→A, where (X,A) is a pair of compact polyhedra. We shall introduce a special Nielsen number,SN(f|ψ), which is a lower bound for the number of fixed points onX-A for all extensions in the homotopy class off. It is shown that for many space pairs this lower bound is the best possible one, and that it can be realized without the by-passing condition.

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Authors and Affiliations

  1. Department of Mathematics, Liaoning University, 110036, Shenyang, China

    Zhao Xuezhi

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  1. Zhao Xuezhi
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Xuezhi, Z. Estimation of the number of fixed points of map extensions. Acta Mathematica Sinica 8, 357–361 (1992). https://doi.org/10.1007/BF02583262

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  • DOI: https://doi.org/10.1007/BF02583262

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