Continua having distal minimal actions by amenable groups

2020/01/11 by Enhui Shi, Shi, Enhui
Mathematics · #37B05 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37B05

paper · pdf · doi:10.48550/arxiv.2001.03755

arXiv admin note: substantial text overlap with arXiv:2001.01183

arxiv created 2020/01/11 · arxiv updated 2020/01/14

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 H¹(X) with integer coefficients is nontrivial. In particular, if X is homotopically equivalent to a CW complex, then X cannot be simply connected.

Citations

• Distal higher rank lattice actions on surfaces

Related

• The non-coexistence of distality and expansivity for group actions on infinite compacta
• Amenable actions, invariant means and bounded cohomology
• Uniform property Γ and the small boundary property
• Every Coxeter group acts amenably on a compact space
• A homological characterization of topological amenability