A 1–parameter family of spherical CR uniformizations of the figure eight knot complement

Deraux, Martin

doi:10.2140/gt.2016.20.3571

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

A $1$–parameter family of spherical CR uniformizations of the figure eight knot complement

Martin Deraux

Geometry & Topology 20 (2016) 3571–3621

DOI: 10.2140/gt.2016.20.3571

Abstract

We describe a simple fundamental domain for the holonomy group of the boundary unipotent spherical CR uniformization of the figure eight knot complement, and deduce that small deformations of that holonomy group (such that the boundary holonomy remains parabolic) also give a uniformization of the figure eight knot complement. Finally, we construct an explicit $1$ –parameter family of deformations of the boundary unipotent holonomy group such that the boundary holonomy is twist-parabolic. For small values of the twist of these parabolic elements, this produces a $1$ –parameter family of pairwise nonconjugate spherical CR uniformizations of the figure eight knot complement.

Keywords

geometric structures, spherical CR structures, complex hyperbolic geometry, discrete groups

Mathematical Subject Classification 2010

Primary: 22E40, 32V05, 57M50

References

Publication

Received: 9 September 2015

Revised: 15 February 2016

Accepted: 18 March 2016

Published: 21 December 2016

Proposed: Walter Neumann

Seconded: Jesper Grodal, Dmitri Burago

Authors

Martin Deraux
Institut Fourier Université Grenoble Alpes 100 rue des maths 38610 Gières France

Volume 20, issue 6 (2016)