The homology of the groupoid of the self-similar infinite dihedral group


  • Eduard Ortega
  • Alvaro Sanchez



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.


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How to Cite

Ortega, E., & Sanchez, A. (2022). The homology of the groupoid of the self-similar infinite dihedral group. MATHEMATICA SCANDINAVICA, 128(2).