Matui's AH conjecture for graph groupoids

  • Petter Nyland

    Department of Mathematical Sciences, Faculty of Information Technology and Electrical Engineering, NTNU - Norwegian University of Science and Technology, Trondheim, Norway
  • Eduard Ortega

    Department of Mathematical Sciences, Faculty of Information Technology and Electrical Engineering, NTNU - Norwegian University of Science and Technology, Trondheim, Norway
Matui's AH conjecture for graph groupoids cover
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Abstract

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 -theory of its groupoid -algebra.

Cite this article

Petter Nyland, Eduard Ortega, Matui's AH conjecture for graph groupoids. Doc. Math. 26 (2021), pp. 1679–1727

DOI 10.4171/DM/853