The homology of the groupoid of the self-similar infinite dihedral group. (English) Zbl 07572343
Summary: 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.
References:
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