On cohomology of the invariant part of an isolating block

Abstract

In this paper we review some old and new results on cohomology of the maximal invariant set inside of an isolating block $B$. In particular, we prove the following one: If $u\cup c v$ is nonzero for some $u\in\overline{H}^*(B)$ and $v\in \overline H^*(B,B^-)$ then the restriction of $u$ to $\overline H^*(S)$ is nontrivial.