An infinite family of hyperbolic graph complements in S^3
Geometric Topology
2007-05-23 v1
Abstract
For any g>1 we construct a graph G_g in S^3 whose exterior M_g supports a complete finite-volume hyperbolic structure with one toric cusp and a connected geodesic boundary of genus g. We compute the canonical decomposition and the isometry group of M_g, showing in particular that any self-homeomorphism of M_g extends to a self-homeomorphism of the pair (S^3,G_g), and that G_g is chiral. Building on a result of Lackenby we also show that any non-meridinal Dehn filling of M_g is hyperbolic, thus getting an infinite family of graphs in S^2xS^1 whose exteriors support a hyperbolic structure with geodesic boundary.
Keywords
Cite
@article{arxiv.math/0309381,
title = {An infinite family of hyperbolic graph complements in S^3},
author = {Roberto Frigerio},
journal= {arXiv preprint arXiv:math/0309381},
year = {2007}
}
Comments
20 pages; 10 figures