Topological Methods in Nonlinear Analysis

The suspension isomorphism for cohomology index braids

Krzysztof P. Rybakowski

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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 $L\colon E\to E$ 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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 29, Number 1 (2007), 1-28.

Dates
First available in Project Euclid: 13 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1463144885

Mathematical Reviews number (MathSciNet)
MR2308214

Zentralblatt MATH identifier
1132.37010

Citation

Rybakowski, Krzysztof P. The suspension isomorphism for cohomology index braids. Topol. Methods Nonlinear Anal. 29 (2007), no. 1, 1--28. https://projecteuclid.org/euclid.tmna/1463144885


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References

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