On the discrete Conley index in the invariant subspace

We present theorems concerning the relations between the discrete homotopy Conley index in the affine invariant subspace and the index calculated in the entire space or in the half space. Our basic tool is the notion of a representable index pair, i.e., an index pair composed of hypercubes. As an application we prove an index theorem for homeomorphisms f : Rn − 1 × [0, +∞) → Rn − 1 × [0, +∞) of compact attraction.