Matui’s AH Conjecture for Graph Groupoids
Peer reviewed, Journal article
Published version
Permanent lenke
https://hdl.handle.net/11250/2979024Utgivelsesdato
2021Metadata
Vis full innførselSamlinger
- Institutt for matematiske fag [2530]
- Publikasjoner fra CRIStin - NTNU [38688]
Originalversjon
10.25537/dm.2021v26.1679-1727Sammendrag
We prove that Matui’s AH conjecture holds for graph groupoids of infinite graphs. This is a conjecture which relates the topological full group of an ample groupoid with the homology of the groupoid. Our main result complements Matui’s result in the finite case, which makes the AH conjecture true for all graph groupoids covered by the assumptions of said conjecture. Furthermore, we observe that for arbitrary graphs, the homology of a graph groupoid coincides with the K-theory of its groupoid C∗-algebra.