A flag structure on a cusped hyperbolic 3-manifold

Elisha Falbel and Rafael Santos Thebaldi

Vol. 278 (2015), No. 1, 51–78

DOI: 10.2140/pjm.2015.278.51

Abstract

A flag structure on a 3-manifold is an $\left(X,G\right)$ structure where $G=SL\left(3,ℝ\right)$ and $X$ is the space of flags on the 2-dimensional projective space. We construct a flag structure on a cusped hyperbolic manifold with unipotent boundary holonomy. The holonomy representation can be obtained from a punctured torus group representation into $SL\left(3,ℝ\right)$ which is equivariant under a pseudo-Anosov.

Keywords

flag structures, hyperbolic structures, SL(3, R) representations

Mathematical Subject Classification 2010

Primary: 57M50

Secondary: 57S30

Milestones

Received: 26 April 2014

Revised: 14 April 2015

Accepted: 14 April 2015

Published: 30 September 2015