Author: Dold, Albrecht

Source: Interdisciplinary Science Reviews, Volume 11, Number 2, June 1986 , pp. 176-180(5)

Publisher: Maney Publishing

Abstract:

Properties of geometrical objects which are invariant under (small) perturbations are a major subject of research in algebraic topology. As a special but typical case the fixed-point equation F(x)=x is discussed here from this point of view. The classical fixed-point index is one such invariant. It turns out to be the universal invariant with respect to a rather natural notion of perturbation. Finer invariants can be obtained if the class of permissible perturbations is restricted. The case of perturbations with symmetries is discussed in more detail.

Document Type: Research Article

DOI: http://dx.doi.org/10.1179/030801886789799665

Affiliations: Mathematical Institute of the University of Heidelberg, FRG

Publication date: 1986-06-01

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