1 4 Ju n 20 04 Normal surfaces in cusped 3 – manifolds

This is the first in a series of papers giving a geometric and combinatorial variant of well–known constructions by Culler, Morgan and Shalen concerning the compactification of the character variety of a 3– manifold. The techniques involve normal surfaces, angle structures and hyperbolic geometry, and lend themselves to the study of surfaces and boundary curves associated to ideal points of the character variety. The subject of this paper is a self–contained treatment of normal surface theory in cusped 3–manifolds with ideal triangulations, presenting a new development of the theory using the induced triangulation of the vertex linking surfaces. AMS Classification 57M25, 57N10