Angle structures and normal surfaces
  Let M be the interior of a compact 3-manifold with non-empty boundary, and T be an ideal (topological) 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 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. 
Feng Luo, Stephan Tillmann