Cohomology of surface minimal sets (Q1961996)

The role of minimal sets in the qualitative theory of dynamical systems is known. Here the author proves that the first integral Čech cohomology of a nontrivial surface minimal set is free abelian of rank at least 2. Thus the result on the rank can be considered as an alternative short proof of the more general fact that any 1D continuum \(Y\) carrying a flow without singular points is a periodic orbit if and only if \(\widetilde H^1(Y)\simeq\mathbb{Z}\), where \(\widetilde H^*\) denotes Čech cohomology with integer coefficients.