Fundamental domains for free groups acting on anti-de Sitter 3-space

2014/10/21 by Jeffrey Danciger, Danciger, Jeffrey, François Guéritaud +3
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1410.5804

28 pages, 2 figures

arxiv created 2014/10/21 · arxiv updated 2014/10/22

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 AdS³; we showed that many properly discontinuous actions of free groups on AdS³ admit fundamental domains bounded by AdS crooked planes. Here we study further the question of which proper actions on AdS³ admit crooked fundamental domains, and show that some do not, in contrast to the Minkowski setting.

Related

• Fundamental domains in the Einstein Universe
• Geometry and topology of complete Lorentz spacetimes of constant curvature
• Extending free group action on surfaces
• Crooked surfaces and anti-de Sitter geometry
• A free action of a finite group on 3-sphere equivalent to a linear action