Fundamental domains for free groups acting on anti-de Sitter 3-space
Geometric Topology
2014-10-22 v1
Abstract
Crooked planes are piecewise linear surfaces that were introduced by Drumm in the early 1990s to construct fundamental domains for properly discontinuous actions of free groups on Minkowski 3-space. In a previous paper, we introduced analogues of these surfaces, called AdS crooked planes, in the 3-dimensional anti-de Sitter space AdS^3; we showed that many properly discontinuous actions of free groups on AdS^3 admit fundamental domains bounded by AdS crooked planes. Here we study further the question of which proper actions on AdS^3 admit crooked fundamental domains, and show that some do not, in contrast to the Minkowski setting.
Keywords
Cite
@article{arxiv.1410.5804,
title = {Fundamental domains for free groups acting on anti-de Sitter 3-space},
author = {Jeffrey Danciger and François Guéritaud and Fanny Kassel},
journal= {arXiv preprint arXiv:1410.5804},
year = {2014}
}
Comments
28 pages, 2 figures