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.
Citation
Anna Gierzkiewicz. Klaudiusz Wójcik. "On the cohomology of an isolating block and its invariant part." Topol. Methods Nonlinear Anal. 32 (2) 313 - 326, 2008.
Information