The AH conjecture for Cantor minimal dihedral systems

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.

arXiv comment12 pages. Improved exposition. Accepted in Mathematica Scandinavica