Uniquely geodesic groups

Abstract: A group is 'uniquely geodesic' (also called 'geodetic') if it admits a locally finite Cayley graphs where any two vertices can be connected by a unique shortest path. Despite this being a very natural geometric property, an algebraic characterisation of uniquely geodetic groups has been elusive for quite some time, even for simple questions such as “are uniquely geodesic groups finitely presented”? We provide the first algebraic classification of uniquely geodesic groups.

This is joint work with Murray Elder, Giles Gardam, Adam Piggott, and Kane Townsend.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( paper )

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Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.

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