Vol. 63, No. 2, 1976

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ISSN: 0030-8730
Nielsen numbers as a homotopy type invariant

Edward Richard Fadell

Vol. 63 (1976), No. 2, 381–388

Let f : X X denote a self map of a compact ANR and let N(f) denote the Nielsen number of f which measures the number of essential fixed points of f. Then it is well-known that f g : X X implies N(f) = N(g). Suppose Y is another ANR and g : Y Y is a map such that for a homotopy equivalence h : X Y , we have hf gh. Then Jiang (1964) proved that in these more general circumstances, Nf = N(g), in the special case when π1(X) is finite. This paper contains a proof of the result without this restriction and applies it to give a technique for extending results in the Nielsen theory of fiber-preserving maps from locally trivial fiber bundles in the category of polyhedra to Hurewicz fibrations in the ANR category.

Mathematical Subject Classification
Primary: 55C20, 55C20
Received: 18 September 1975
Published: 1 April 1976
Edward Richard Fadell