Geodesic
Higher-dimensional digraphs from cube complexes and their spectral theory
Nadia S. Larsen1 ; Alina Vdovina2 orcid
1University of Oslo, Oslo, Norway
2City College of New York, New York, USA
Groups, geometry, and dynamics, Tome 18 (2024) no. 4, pp. 1427-1467

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DOI

We define k-dimensional digraphs and initiate a study of their spectral theory. The k-dimensional digraphs can be viewed as generating graphs for small categories called k-graphs. Guided by geometric insight, we obtain several new series of k-graphs using cube complexes covered by Cartesian products of trees, for k≥2. These k-graphs can not be presented as virtual products and constitute novel models of such small categories. The constructions yield rank-k Cuntz–Krieger algebras for all k≥2. We introduce Ramanujan k-graphs satisfying optimal spectral gap property and show explicitly how to construct the underlying k-digraphs.
DOI : 10.4171/ggd/787
Classification : 47D03, 20J99
Mots-clés : higher-dimensional digraphs, cube complexes, C∗-algebras

Nadia S. Larsen  1   ; Alina Vdovina  2

1 University of Oslo, Oslo, Norway
2 City College of New York, New York, USA 
Nadia S. Larsen; Alina Vdovina. Higher-dimensional digraphs from cube complexes and their spectral theory. Groups, geometry, and dynamics, Tome 18 (2024) no. 4, pp. 1427-1467. doi: 10.4171/ggd/787
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