The Maximal Tube under the Deformations of a Class of 3-dimensional Hyperbolic Cone-manifolds

  • SUHYOUNG CHOI
  • Published 2004

Abstract

Recently, Hodgson and Kerckhoff found a small bound on Dehn surgered 3-manifolds from hyperbolic knots not admitting hyperbolic structures using deformations of hyperbolic cone-manifolds. They asked whether the area normalized meridian length squared of maximal tubular neighborhoods of the singular locus of the cone-manifold is decreasing and that summed with the cone angle squared is increasing as we deform the cone-angles. We confirm this near 0 cone-angles for an infinite family of hyperbolic conemanifolds obtained by Dehn surgeries along the Whitehead link complements. The basic method is based on explicit holonomy computations using the Apolynomials and finding the maximal tubes. One of the key tool is the Taylor expression of a geometric component of the zero set of the A-polynomial in terms of the cone-angles. We also show a sequence of Taylor expressions for Dehn surgered manifolds converges to one for the limit hyperbolic manifold.

11 Figures and Tables

Cite this paper

@inproceedings{CHOI2004TheMT, title={The Maximal Tube under the Deformations of a Class of 3-dimensional Hyperbolic Cone-manifolds}, author={SUHYOUNG CHOI}, year={2004} }