Continua having distal minimal actions by amenable groups

Abstract

Let $X$ be a non-degenerate connected compact metric space. If $X$ admits a distal minimal action by a finitely generated amenable group, then the first \vCech cohomology group ${\check{H}}^1(X)$ with integer coefficients is nontrivial. In particular, if $X$ is homotopically equivalent to a CW complex, then $X$ cannot be simply connected.

arXiv admin note: substantial text overlap with arXiv:2001.01183

References in corpus (1)

• Distal higher rank lattice actions on surfaces

Cited by in corpus (1)

• The non-coexistence of distality and expansivity for group actions on infinite compacta