Geodesic
Matui's AH conjecture for graph groupoids
Documenta mathematica, Tome 26 (2021), pp. 1679-1727.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 22A22, 05C63, 19D55, 37B05, 46L05
Keywords: ample groupoid, homology of étale groupoids, topological full group, graph groupoid, AF-groupoid, graph \(C^*\)-algebra 
@article{DOCMA_2021__26__a11,
     author = {Nyland, Petter and Ortega, Eduard},
     title = {Matui's {AH} conjecture for graph groupoids},
     journal = {Documenta mathematica},
     pages = {1679--1727},
     publisher = {mathdoc},
     volume = {26},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a11/}
}
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Nyland, Petter; Ortega, Eduard. Matui's AH conjecture for graph groupoids. Documenta mathematica, Tome 26 (2021), pp. 1679-1727. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a11/