TY - JOUR AU - Ortega, Eduard AU - Sanchez, Alvaro PY - 2022/06/11 Y2 - 2024/03/28 TI - The homology of the groupoid of the self-similar infinite dihedral group JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 128 IS - 2 SE - Articles DO - 10.7146/math.scand.a-129708 UR - https://www.mscand.dk/article/view/129708 SP - AB - <p>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.</p> ER -