Type: Seminar

Distribution: World

Expiry: 13 Feb 2017

CalTitle1: Computational techniques for proving that a group is hyperbolic

Auth: donnelly@seurat.maths.usyd.edu.au

Speaker: Derek Holt (University of Warwick). Title: Computational techniques for proving that a group is hyperbolic. Abstract: A finitely presented group is called hyperbolic if geodesic triangles in its Cayley graph are uniformly thin or, equivalently, if its Dehn function is linear. The programs in the author’s KBMAG package, which is implemented in Magma, can verify hyperbolicity of a given finitely presented group. In this talk we describe new methods for proving hyperbolicity and for estimating the Dehn function that are based on small cancellation theory and the analysis of the curvature of van Kampen diagrams for the group. The first version of a Magma implementation is available. These methods are due to Richard Parker and many others. They have the disadvantage that they are not guaranteed to succeed on every hyperbolic group presentation, but when they do they are generally much faster than KBMAG. They can also sometimes be carried out by hand on infinite families of presentations, whereas KBMAG can only be applied to individual presentations.