Angle structures and normal surfaces

Let M be the interior of a compact 3-manifold with boundary, and let T be an ideal triangulation of M. This paper describes necessary and sufficient conditions for the existence of angle structures, semi-angle structures and generalised angle structures on (M; T ) respectively in terms of a generalised Euler characteristic function on the solution space of the normal surface theory of (M; T ). This extends previous work of Kang and Rubinstein, and is itself generalised to a more general setting for 3-dimensional pseudo-manifolds.