Negative curvature in graphical small cancellation groups

@article{Arzhantseva2016NegativeCI,
title={Negative curvature in graphical small cancellation groups},
author={G. Arzhantseva and Christopher H. Cashen and D. Gruber and D. Hume},
journal={arXiv: Group Theory},
year={2016}
}

We use the interplay between combinatorial and coarse geometric versions of negative curvature to investigate the geometry of infinitely presented graphical $Gr'(1/6)$ small cancellation groups. In particular, we characterize their 'contracting geodesics', which should be thought of as the geodesics that behave hyperbolically.
We show that every degree of contraction can be achieved by a geodesic in a finitely generated group. We construct the first example of a finitely generated group $G… CONTINUE READING