Vol. 106, No. 1, 1983

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On the computations of the Nielsen number

Boju Jiang

Vol. 106 (1983), No. 1, 105–113
Abstract

The aim of this note is to show the following

Main Theorem. Let X be a compact connected ANR, f : X X be a map. Suppose there is an integer n such that fπn(π1(X)) J(fn). Then any two fixed point classes of f have the same index. Hence

L(f) = 0 implies N(f) = 0, while
L(f)0 implies N(f) = Coker(H1(X)1−−f→∗H1(X)).
Here L(f) and N(f) are the Lefschetz number and Nielsen number of f respectively, and J(F) π1(X) stands for the Jiang subgroup of f.

Mathematical Subject Classification 2000
Primary: 55M20
Milestones
Received: 29 September 1981
Published: 1 May 1983
Authors
Boju Jiang