An approach to the shape Conley index without index pairs

摘要: Robbin and Salamon proved that the shape of homotopy Conley index an isolated invariant set K coincides with one–point compactification unstable region Wu(K) endowed a certain topology which they called intrinsic topology. In this paper equivalent, simplified definition latter is given in elementary terms, without resorting to pairs whatsoever. We then show how our approach allows for development its basic properties pair–free fashion simplifies some classical constructions, such as Morse equations decomposition. As final application, embrionary work about geometry Wu(K)/K presented together argument may contribute understanding relations between attractor sits basin attraction complexity dynamics latter.