Universal manifold pairings and positivity

@article{Freedman2005UniversalMP,
  title={Universal manifold pairings and positivity},
  author={Michael H. Freedman and Alexei Y. Kitaev and C. Nayak and Johannes K. Slingerland and Kevin Walker and Zhenghan Wang},
  journal={Geometry \& Topology},
  year={2005},
  volume={9},
  pages={2303-2317}
}
Gluing two manifolds M1 and M2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x = �aiMi yields a sesquilinear pairing p = h , i with values in (formal linear combinations of) closed manifolds. Topological quantum field theory (TQFT) represents this universal pairing p onto a finite dimensional quotient pairing q with values in C which in physically motivated cases is positive definite. To see if such a “unitary” TQFT can potentially detect any… 

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