Seminar

We will tell the story of affine deformations of surfaces with fundamental group of F_2 from the Lorentzian geometry point of view. In particular, the space of proper affine deformations of these surfaces is tiled by the affine deformations corresponding to a basis (or superbasis) of the underlying linear group. In the case of the three-holed sphere and the two-holed cross surface, there is one tile. The tiling of the space of proper affine deformations of the one-holed torus is much richer and mimics the Farey tessellation of the hyperbolic plane.

This story will have a Prologue.  We will give a nuts and bolts introduction to crooked planes, how to put them together into « ideal triangulations », and how to pull them apart in disjoint configurations.