Angle structures and normal surfaces

Abstract

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