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arXiv · 2310.15953

Bakry-Émery and Ollivier Ricci Curvature of Cayley Graphs

David Cushing·Supanat Kamtue·Riikka Kangaslampi·Shiping Liu·Florentin Münch·Norbert Peyerimhoff
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Abstract

In this article we study two discrete curvature notions, Bakry-Émery curvature and Ollivier Ricci curvature, on Cayley graphs. We introduce Right Angled Artin-Coxeter Hybrids (RAACHs) generalizing Right Angled Artin and Coxeter groups (RAAGs and RACGs) and derive the curvatures of Cayley graphs of certain RAACHs. Moreover, we show for general finitely presented groups $Γ= \langle S \, \mid\, R \rangle$ that addition of relators does not lead to a decrease the weighted curvatures of their Cayley graphs with adapted weighting schemes.

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David Cushing, Supanat Kamtue, Riikka Kangaslampi, Shiping Liu, Florentin Münch, Norbert Peyerimhoff. 2023-10-24. Bakry-Émery and Ollivier Ricci Curvature of Cayley Graphs. https://arxiv.org/abs/2310.15953

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