On the cohomology of an isolating block and its invariant part

Anna Gierzkiewicz, Klaudiusz Wójcik

DOI: http://dx.doi.org/10.12775/TMNA.2008.050

Abstract


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.

Keywords


Isolating block; Conley index

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