@article{Ortega_Sanchez_2022, title={The homology of the groupoid of the self-similar infinite dihedral group}, volume={128}, url={https://www.mscand.dk/article/view/129708}, DOI={10.7146/math.scand.a-129708}, abstractNote={<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>}, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={Ortega, Eduard and Sanchez, Alvaro}, year={2022}, month={Jun.} }