Positivity of the universal pairing in 3 dimensions

@article{Calegari2008PositivityOT,
  title={Positivity of the universal pairing in 3 dimensions},
  author={Danny Calegari and Michael H. Freedman and Kevin Walker},
  journal={Journal of the American Mathematical Society},
  year={2008},
  volume={23},
  pages={107-188}
}
Associated to a closed, oriented surface S is the complex vector space with basis the set of all compact, oriented 3-manifolds which it bounds. Gluing along S defines a Hermitian pairing on this space with values in the complex vector space with basis all closed, oriented 3-manifolds. The main result in this paper is that this pairing is positive, i.e. that the result of pairing a nonzero vector with itself is nonzero. This has bearing on the question of what kinds of topological information… 
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