### On the cohomology of an isolating block and its invariant part

#### 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.

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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