Convex Decomposition Theory

  title={Convex Decomposition Theory},
  author={WILLIAM H. KAZEZ and Gordana M Mati{\'c}},
We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many nonisotopic, nonisomorphic tight contact structures. It has been known for some time that there are deep connections between the theory of taut foliations and tight contact structures due to the work of Eliashberg and Thurston [7]. In particular, they proved that a… CONTINUE READING
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