The homology of the groupoid of the self-similar dihedral group
Peer reviewed, Journal article
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Date
2022Metadata
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- Institutt for matematiske fag [2438]
- Publikasjoner fra CRIStin - NTNU [38034]
Abstract
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.