Higher-dimensional digraphs from cube complexes and their spectral theory
Nadia S. Larsen
University of Oslo, Oslo, NorwayAlina Vdovina
City College of New York, New York, USA
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Abstract
We define -dimensional digraphs and initiate a study of their spectral theory. The -dimensional digraphs can be viewed as generating graphs for small categories called -graphs. Guided by geometric insight, we obtain several new series of -graphs using cube complexes covered by Cartesian products of trees, for . These -graphs can not be presented as virtual products and constitute novel models of such small categories. The constructions yield rank- Cuntz–Krieger algebras for all . We introduce Ramanujan -graphs satisfying optimal spectral gap property and show explicitly how to construct the underlying -digraphs.
Cite this article
Nadia S. Larsen, Alina Vdovina, Higher-dimensional digraphs from cube complexes and their spectral theory. Groups Geom. Dyn. (2024), published online first
DOI 10.4171/GGD/787