Branched Spherical CR structures on the complement of the figure eight knot
Geometric Topology
2013-04-02 v1
Abstract
We obtain a branched spherical CR structure on the complement of the figure eight knot with a given holonomy representation (called rho_2). There are essentially two boundary unipotent representations from the complement of the figure eight knot into PU(2,1), we call them rho_1 and rho_2. We make explicit some fundamental differences between these two representations. For instance, seeing the figure eight knot complement as a surface bundle over the circle, the behaviour of of the fundamental group of the fiber under the representation is a key difference between rho_1 and rho_2.
Keywords
Cite
@article{arxiv.1304.0112,
title = {Branched Spherical CR structures on the complement of the figure eight knot},
author = {Elisha Falbel and Jieyan Wang},
journal= {arXiv preprint arXiv:1304.0112},
year = {2013}
}