Abstract

We show that a properly immersed thrice-punctured sphere in a cusped orientable hyperbolic 3-manifold is either embedded or has a single clasp in a manifold that is the Whitehead link complement or obtained by hyperbolic Dehn filling on a cusp of the Whitehead link complement.

Keywords

hyperbolic geometry, topology, immersion

Mathematical Subject Classification

Primary: 30F40, 57M50

Milestones

Received: 19 February 2008
Accepted: 4 September 2008

Authors