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A Nielsen theory for intersection numbers

100%

McCord C. K.

Fundamenta Mathematicae

1997

tom 152

nr 2

117-150

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.

Wecken theorems for Nielsen intersection theory

100%

McCord C. K.

Banach Center Publications

1999

tom 49

nr 1

235-252

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. Recently, the techniques of Nielsen theory have been applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f,g), was introduced, and shown to have many of the properties analogous to those of the Nielsen fixed point number. In particular, it is a homotopy-invariant lower bound for the number of intersections of a pair of maps. The question of whether or not this lower bound is sharp can be thought of as the Wecken problem for intersection theory. In this paper, the Wecken problem for intersections is considered, and some Wecken theorems are proved.

Ograniczanie wyników

1 Banach Center Publications

1 Fundamenta Mathematicae

2 McCord C. K.

1 1999

1 1997

Wyniki wyszukiwania

A Nielsen theory for intersection numbers

Wecken theorems for Nielsen intersection theory