** "Geometry and Analysis on Groups" Research Seminar **

Graphical small cancellation is a construction that allows us to build a finitely generated group containing a prescribed sequence of graph in its Cayley graph. If the sequence of graphs is less and less hyperbolic then the resulting group is not hyperbolic. We prove a local-to-global result that says that for a geodesic \(\alpha\) in the Cayley graph of a graphical small cancellation group \(G\), if the intersection of \(\alpha\) with each copy of a component of the defining graph is uniformly contracting, then \(\alpha\) is contracting in the Cayley graph of \(G\).

This is joint work with Arzhantseva, Gruber, and Hume.