Wecken's theorem for periodic points in dimension at least 3 (Q2493892)
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| Language | Label | Description | Also known as |
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| English | Wecken's theorem for periodic points in dimension at least 3 |
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Wecken's theorem for periodic points in dimension at least 3 (English)
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16 June 2006
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\textit{Boju Jiang} [Contemp. Math. 14 (1983; Zbl 0512.55003)] introduced a homotopy invariant \(NF_n(f)\) which is a lower bound for the cardinality of periodic points of period \(n\) for a self-map \(f\) of a compact polyhedron. The present author in [Topology 42, 1101--1124 (2003; Zbl 1026.55001) and ``Wecken's theorem for fixed and periodic points'', in Handbook of Topological fixed point theory, 555--616 (2005; Zbl 1079.55007)] using rather tricky geometric arguments showed that any selfmap \(f:M\to M\) of a compact PL-manifold of dimension at least 3 is homotopic to a map \(g\) such that \(g^n\) has precisely \(NF_n(f)\) fixed points. Here, he gives a much simpler proof of this result adapting a method due to \textit{Boju Jiang} [Lect. Notes Math. 886, 163--170 (1981; Zbl 0482.57014)] to the case of periodic points.
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fixed point
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periodic point
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fixed point index
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Lefschetz number
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Nielsen number
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