TY - JOUR
AU - Rybakowski, Krzysztof P.
PY - 2007/03/01
Y2 - 2024/04/15
TI - The suspension isomorphism for cohomology index braids
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 29
IS - 1
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2007.001
SP - 1 - 28
AB - Let $X$ be a metric space, $\pi$ be a localsemiflow on $X$, $k\in{\mathbb N}$, $E$ be a $k$-dimensional normed real vector space and $\widetilde\pi$ be the semiflow generated by theequation $\dot y=Ly$, where $L\co E\to E$ is a linear mapwhose all eigenvalues have positive real parts. We show inthis paper that for every admissible isolated$\pi$-invariant set $S$ there is a well-defined isomorphismof degree $k$ from the (Alexander-Spanier)-cohomologycategorial 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 ofthese isomorphisms commutes with cohomology indexsequences. This extends previous results by Carbinatto andRybakowski to the Alexander-Spanier-cohomologycase.
ER -