On cohomology of the invariant part of an isolating block. (English) Zbl 0953.54037

Srzednicki, Roman

Topol. Methods Nonlinear Anal. 14, No. 2, 257-260 (1999).

Summary: 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: If \(u\cup cv\) 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.

MSC:

54H20	Topological dynamics (MSC2010)
37C10	Dynamics induced by flows and semiflows

Keywords:

Ważewski retract; Alexander-Spanier cohomology; isolating block