Vol. 100, No. 1, 1982

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Fixed point classes of a fiber map

Cheng Ye You

Vol. 100 (1982), No. 1, 217–241

Let (E,p,B) be a fiber space with E, B and all fibers compact connected ANR’s. Let f : E E be a fiber map, then f induces f : B B. For each fixed point b of f, we define fb = f|p1(b) : p1(b) p1(b). Then p f = f p and ib fb = f ib, where ib is the inclusion map. We have Nielsen numbers N(f), N(f) and N(fb). A product formula relating these Nielsen numbers was published by Brown in 1967. There have been several improvements of the formula since that time.

In this paper, we study the structure of the fixed point classes of f, and prove some theorems about the product formula of the Nielsen number of a fiber map, which imply results of Fadell and of Pak.

Mathematical Subject Classification 2000
Primary: 55R05
Secondary: 55M20
Received: 22 October 1980
Published: 1 May 1982
Cheng Ye You