ESSENTIAL NORMAL AND SPUN NORMAL SURFACES IN 3-MANIFOLDS

Abstract

Normal and spun normal surfaces are key tools for algorithms in 3-dimensional geometry and topology, especially concerning essential surfaces. In a recent paper of Dunfield and Garoufalidis, an interesting criterion is given for a spun normal surface to be essential in an ideal triangulation of a 3-manifold with a complete hyperbolic metric of finite volume. Their method uses ideal points of character varieties and Culler–Shalen theory. In this paper, we give a simple proof of a criterion which applies for both triangulations of closed 3-manifolds and ideal triangulations of the interior of compact 3-manifolds, giving a sufficient condition for a normal or a spun normal surface to be essenti..