Normal surfaces in topologically finite 3-manifolds

Abstract

The concept of a normal surface in a triangulated, compact 3-manifold was generalised by Thurston to a spun-normal surface in a non-compact 3-manifold with ideal triangulation. This paper defines a boundary curve map which takes a spun-normal surface to an element of the direct sum of the first homology groups of the vertex linking surfaces. The boundary curve map is used to study the topology of a spun-normal surface as well as to determine the dimension of the projective solution space of the algebraic equations arising from the quadrilateral coordinates of spun-normal surfaces.