Dr Ioannis Ivrissimtzis ioannis.ivrissimtzis@durham.ac.uk
Associate Professor
Trivalent expanders, $(Delta – Y)$-transformation, and hyperbolic surfaces
Ivrissimtzis, Ioannis; Peyerimhoff, Norbert; Vdovina, Alina
Authors
Professor Norbert Peyerimhoff norbert.peyerimhoff@durham.ac.uk
Professor
Alina Vdovina
Abstract
We construct a new family of trivalent expanders tessellating hyperbolic surfaces with large isometry groups. These graphs are obtained from a family of Cayley graphs of nilpotent groups via (Delta–Y)-transformations. We study combinatorial, topological and spectral properties of our trivalent graphs and their associated hyperbolic surfaces. We compare this family with Platonic graphs and their associated hyperbolic surfaces and see that they are generally very different with only one hyperbolic surface in the intersection. Finally, we provide a number theory free proof of the Ramanujan property for Platonic graphs and a special family of subgraphs.
Citation
Ivrissimtzis, I., Peyerimhoff, N., & Vdovina, A. (2019). Trivalent expanders, $(Delta – Y)$-transformation, and hyperbolic surfaces. Groups, Geometry, and Dynamics, 13(3), 1103-1131. https://doi.org/10.4171/ggd/518
Journal Article Type | Article |
---|---|
Online Publication Date | Jul 1, 2019 |
Publication Date | Jul 1, 2019 |
Deposit Date | Aug 8, 2019 |
Publicly Available Date | Jul 1, 2020 |
Journal | Groups, Geometry, and Dynamics |
Print ISSN | 1661-7207 |
Publisher | EMS Press |
Peer Reviewed | Peer Reviewed |
Volume | 13 |
Issue | 3 |
Pages | 1103-1131 |
DOI | https://doi.org/10.4171/ggd/518 |
Files
Accepted Journal Article
(304 Kb)
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