An infinite family of hyperbolic graph complements in S^3

Details An infinite family of hyperbolic graph complements in S^3 An infinite family of hyperbolic graph complements in S^3

2003-09-23

arxiv.org/abs/math/0309381v1

J. Knot Theory Ramifications 14 (2005), 479--496.

Mathematics

Geometric Topology

20 pages; 10 figures

Scientific paper

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.

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