Vol. 66, No. 1, 1976

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An estimate of the Nielsen number and an example concerning the Lefschetz fixed point theorem

Dan McCord

Vol. 66 (1976), No. 1, 195–203

Given a map f : X X of a compact ANR and any finite connected regular covering p : X X to which f admits lifts, then one can compute a certain homotopy invariant NH(f) if the Lefschetz numbers of the lifts and the relation of the lifts to the covering transformations are known. H = p#π1(X). Every map homotopic to f has at least NH(f) fixed points. If X is a finite polyhedron, then NH(f) N(f), the Nielsen number. The smaller invariant is easier to compute by virtue of its smallness, but it is adequate to discern for example homeomorphisms, h, of manifolds in all dimensions with L(h) = 0 and N(h) 2.

Mathematical Subject Classification
Primary: 55C20, 55C20
Received: 18 February 1976
Revised: 26 May 1976
Published: 1 September 1976
Dan McCord