The suspension isomorphism for cohomology index braids

Abstract

Let $X$ be a metric space, $\pi$ be a local
semiflow on $X$, $k\in{\mathbb N}$, $E$ be a $k$-dimensional normed real vector
space and $\widetilde\pi$ be the semiflow generated by the
equation $\dot y=Ly$, where $L\co E\to E$ is a linear map
whose all eigenvalues have positive real parts. We show in
this paper that for every admissible isolated
$\pi$-invariant set $S$ there is a well-defined isomorphism
of degree $k$ from the (Alexander-Spanier)-cohomology
categorial Conley-Morse index of $(\pi,S)$
to the cohomology categorial Conley-Morse index of
$(\pi\times\widetilde\pi,S\times\{0\})$ such that the family of
these isomorphisms commutes with cohomology index
sequences. This extends previous results by Carbinatto and
Rybakowski to the Alexander-Spanier-cohomology
case.