August 16, 2025Open Access

Bakry-Émery and Ollivier Ricci Curvature of Cayley Graphs

Key Points

Bakry-Émery and Ollivier Ricci curvatures are analyzed in cayley graphs based on RAACHs.
Addition of relators in finitely presented groups does not decrease their weighted curvatures.
Cayley graph curvature is derived from right angled artin and coxeter groups using adapted weighting schemes.
The findings highlight the robustness of curvature under specific group modifications, supporting further exploration.

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 = S \, \, R that addition of relators does not lead to a decrease in the weighted curvatures of their Cayley graphs with adapted weighting schemes.

Bakry-Émery and Ollivier Ricci Curvature of Cayley Graphs

Key Points

Abstract

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