Nielsen fixed point theory (Q2776339)

This very well-written paper consists of two parts. In the first, the author presents a substantially self-contained exposition of the Reidemeister trace of a self-map of a compact manifold (or, more generally, a compact ENR). The Reidemeister trace is the key concept of topological fixed point theory; it generalizes both the classical Lefschetz number and the Nielsen number that furnishes a lower bound for the number of fixed points of all maps homotopic to the given one. This part also contains an attractive proof of a Wecken-type theorem, that a map on a compact \(n\)-manifold, for \(n\) at least 4, is homotopic to a map with exactly the Nielsen number of fixed points. In the second part, the author presents some topics from topological fixed point theory that, as he writes, ``suggest some reasons geometric topologists should pay attention to Nielsen theory''. In addition to a careful exposition of the mathematical content, the author includes comments that will guide the reader to some of the relevant literature.NEWLINENEWLINEFor the entire collection see [Zbl 0977.00029].