Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, March 5, 2018 - 12:00 to 13:00

Location:

Stag 110

Abstract:

Take a regular 2n-sided hyperbolic polygon and use isometric copies of it to tile the hyperbolic plane. The torsion-free groups which act on the plane by cellular isometries, and simply transitively on the set of vertices, correspond to the hyperbolic surface groups, which have been extensively studied. The hyperbolic plane, tiled in this manner, is a special case of a cellular metric space called a 2-dimensional hyperbolic building. In this talk, we will explore properties of torsion-free groups of cellular isometries of 2-dimensional hyperbolic buildings acting simply transitively on vertices, and present a straightforward algorithm by which they can be classified up to isomorphism.