"Geometry and Analysis on Groups" Research Seminar

Time: 2015.10.27, 15:00--17:00
Location: Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Contracting geodesics in graphical small cancellation groups."
Speaker: Christopher Cashen (Universität Wien)
Abstract: We define a geodesic $$\alpha$$ to be ‘contracting’ if the diameter of the closest point projection to $$\alpha$$ of any ball is asymptotically much smaller than the diameter of the ball. A geodesic is contracting if and only if it is Morse, which is a property enjoyed, for instance, by geodesics in hyperbolic spaces.

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.