## A Nielsen theory for intersection numbers

### Volume 152 / 1997

Fundamenta Mathematicae 152 (1997), 117-150
DOI: 10.4064/fm-152-2-117-150

#### Abstract

Nielsen theory, originally developed as a homotopy-theoretic approach to fixed point theory, has been translated and extended to various other problems, such as the study of periodic points, coincidence points and roots. In this paper, the techniques of Nielsen theory are applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f,g), is introduced, and shown to have many of the properties analogous to those of the Nielsen fixed point number. In particular, NI(f,g) gives a lower bound for the number of points of intersection for all maps homotopic to f and g.