On the cohomology of an isolating block and its invariant part
Keywords
Isolating block, Conley indexAbstract
We give a sufficient condition for the existence of an isolating block $B$ for an isolated invariant set $S$ such that the inclusion induced map in cohomology $H^* (B)\to H^*(S)$ is an isomorphism. We discuss the Easton's result concerning the special case of flows on a $3$-manifold. We prove that if $S$ is an isolated invariant set for a flow on a $3$-manifold and $S$ is of finite type, then each isolating neighbourhood of $S$ contains an isolating block $B$ such that $B$ and $B^-$ are manifolds with boundary and the inclusion induced map in cohomology is an isomorphism.Downloads
Published
2008-12-01
How to Cite
1.
GIERZKIEWICZ, Anna and WÓJCIK, Klaudiusz. On the cohomology of an isolating block and its invariant part. Topological Methods in Nonlinear Analysis. Online. 1 December 2008. Vol. 32, no. 2, pp. 313 - 326. [Accessed 12 December 2024].
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