2013/03/30 by Elisha Falbel, Falbel, Elisha, Jieyan Wang +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT
paper · pdf · doi:10.48550/arxiv.1304.0112
arxiv created 2013/03/30 · openalex publication_date 2013/03/30 · arxiv updated 2013/04/02 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We obtain a branched spherical CR structure on the complement of the figure eight knot with a given holonomy representation (called rho2). There are essentially two boundary unipotent representations from the complement of the figure eight knot into PU(2,1), we call them rho1 and rho2. 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 rho1 and rho2.