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Transactions of the American Mathematical Society

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Angle structures and normal surfaces


Authors: Feng Luo and Stephan Tillmann
Journal: Trans. Amer. Math. Soc. 360 (2008), 2849-2866
MSC (2000): Primary 57M25, 57N10
DOI: https://doi.org/10.1090/S0002-9947-08-04301-8
Published electronically: January 7, 2008
MathSciNet review: 2379778
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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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Additional Information

Feng Luo
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854
Email: fluo@math.rutgers.edu

Stephan Tillmann
Affiliation: Départment de mathématiques, Université du Québec à Montréal, Case postale 8888, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3P8
Email: tillmann@math.uqam.ca

DOI: https://doi.org/10.1090/S0002-9947-08-04301-8
Keywords: 3--manifold, ideal triangulation, angle structure
Received by editor(s): December 5, 2005
Published electronically: January 7, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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