On Metrics for Quandles and Schreier Graphs

par Kohei IWAMOTO (Ritsumeikan University)

vendredi 11 sept. 2026, 11:15 → 12:15 Europe/Paris

112 (ICJ)

A quandle is an algebraic structure that generalizes the conjugation operation in groups and has been studied in connection with knot theory, symmetric space theory, and related areas. On the other hand, in geometric group theory, Cayley graphs and word metrics associated with finitely generated groups are fundamental tools for studying the large-scale geometry of groups.

 

In this talk, with the aim of introducing ideas from geometric group theory into quandle theory, we construct Schreier graphs from natural group actions associated with quandles and introduce metrics on their connected components.

 

In the first part of the talk, we recall the definition of a quandle and present several examples. We introduce Schreier graphs, which generalize Cayley graphs, and explain the metrics induced by these graphs. We also introduce the notion of quasi-isometry and show that each connected component of a quandle naturally determines a quasi-isometry class. 

 

This talk is based on joint work with Ryoya Kai (Nara University of Education) and Yuya Kodama (Kagoshima University).