Angle structures and normal surfaces

Luo, Feng; Tillmann, Stephan

doi:10.1090/S0002-9947-08-04301-8

Angle structures and normal surfaces
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by Feng Luo and Stephan Tillmann PDF

Trans. Amer. Math. Soc. 360 (2008), 2849-2866 Request permission

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.

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