Article ID Journal Published Year Pages File Type
4660674 Topology and its Applications 2006 17 Pages PDF
Abstract

The purpose of this article is to show that the image of the homological boundary map attached to a filtration for an attractor–repeller pair of a smooth flow on a compact manifold is a submodule of the Alexander cohomology of certain order of the connecting set (some restrictions have to be imposed in order to have a valid argument). In particular, this gives an affirmative answer to a conjecture in Conley index theory which states that if the boundary map is not zero in two dimensions, the connecting set cannot be contractible.

Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology