The suspension isomorphism for homology index braids - Carbinatto, Maria C.; Rybakowski, Krzysztof P. (Topological Methods in Nonlinear Analysis, 2006)
Let X be a metric space, π be a local semiflow on X, kN, E be a k-dimensional normed space and π be the semiflow generated by the equation y=Ly, where LE→ E is a linear map whose all eigenvalues have positive real parts. We show in this paper that for every admissible isolated π-invariant set S there is a well-defined isomorphism of degree -k from the homology categorial Conley-Morse index of (π×π,S×{0}) to the homology categorial Conley-Morse index of (π,S) such that the family of these isomorphisms commutes with homology index sequences. In particular, given a partially ordered Morse decomposition (M_i)_iP of S there is an isomorphism of degree -k from the homology index braid of (M_i×{0})_iP to the homology index braid of (M_i)_iP, so C-connection matrices of (M_i×{0})_iP are just C-connection matrices of (M_i)_iP shifted by k to the right.