Angle structures and normal surfaces

2005/10/25 by Feng Luo, Stephan Tillmann, Luo, Feng +1
Mathematics · #57M25 #57N10 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25 #msc:57N10

paper · pdf · doi:10.48550/arxiv.math/0510537

17 pages, 3 figures, to appear in Trans. Amer. Math. Soc

arxiv created 2006/06/05 · arxiv updated 2009/12/01

Abstract

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.

Related

• Angle structures on pseudo 3-manifolds
• Angle structure on general hyperbolic 3-manifolds
• Angle structures on 3-manifolds
• Normal surfaces in topologically finite 3-manifolds
• Ideal triangulations of 3--manifolds I: spun normal surface theory