The homology of the groupoid of the self-similar infinite dihedral group - Ortega, Eduard; Sanchez, Alvaro (MATHEMATICA SCANDINAVICA, 2022)
We compute the $K$-theory of the $C^*$-algebra associated to the self-similar infinite dihedral group, and the homology of its associated étale groupoid. We see that the rational homology differs from the $K$-theory, strongly contradicting a conjecture posted by Matui. Moreover, we compute the abelianization of the topological full group of the groupoid associated to the self-similar infinite dihedral group.