Uniquely geodesic groups are virtually free

21.11.2023 15:00 - 17:00

Davide Spriano (Oxford)

 In geometry, a very desirable property is the existence of a unique geodesic between any two points. When turning to graph theory, however, this property is not well understood. More precisely, we say that a graph is uniquely geodesic if for any two vertices there exists a unique shortest path between them. The goal of this talk is to provide structural results for uniquely geodesic graph and show that groups with a uniquely geodesic Cayley graph are virtually free. This is joint work with Elder, Gardam, Piggott, and Townsend.


G. Arzhantseva, Ch. Cashen


SR 8, 2. OG, OMP 1