The AH conjecture for Cantor minimal dihedral systems

2022/06/22 by Scarparo, Eduardo
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2206.11179

Abstract

The AH conjecture relates the low-dimensional homology groups of a groupoid with the abelianization of its topological full group. We show that transformation groupoids of minimal actions of the infinite dihedral group on the Cantor set satisfy this conjecture. The proof uses Kakutani-Rokhlin partitions adapted to such systems.

Related

• Matui's AH conjecture for Graph Groupoids
• The homology of the groupoid of the self-similar dihedral group
• Almost finiteness and homology of certain non-free actions
• Etale groupoids arising from products of shifts of finite type
• Ample groupoids: equivalence, homology, and Matui's HK conjecture