Angle structures and normal surfaces

Abstract

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