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

2020/11/04 by Eduard Ortega, Álvaro Sánchez, Ortega, Eduard +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric and Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2011.02554

openalex publication_date 2020/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an example of a locally compact effective Hausdorff, minimal ample groupoid such that its rational homology differs from the K-theory of its reduced groupoid C^*-algebra. Moreover, we prove that such example satisfies Matui's AH-conjecture.

Citations

• Self-Similar Graphs
• Ample groupoids: equivalence, homology, and Matui's HK conjecture

Related

• Ample groupoids: equivalence, homology, and Matui's HK conjecture
• Homology and K-theory for self-similar actions of groups and groupoids
• A non-amenable groupoid whose maximal and reduced C^*-algebras are the same
• Matui's AH conjecture for Graph Groupoids
• Homology of the Katsura-Exel-Pardo groupoid