The Thurston norm via normal surfaces

@article{Cooper2007TheTN,
  title={The Thurston norm via normal surfaces},
  author={Daryl Cooper and Stephan Tillmann},
  journal={Pacific Journal of Mathematics},
  year={2007},
  volume={239},
  pages={1-15}
}
Given a triangulation of a closed, oriented, irreducible, atoroidal 3-manifold every oriented, incompressible surface may be isotoped into normal position relative to the triangulation. Such a normal oriented surface is then encoded by nonnegative integer weights, 14 for each 3-simplex, that describe how many copies of each oriented normal disc type there are. The Euler characteristic and homology class are both linear functions of the weights. There is a convex polytope in the space of weights… 
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