"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 (Universitšt 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.