# 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…

## 26 Citations

Positivity of the universal pairing in 3 dimensions

- Mathematics
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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…

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AbstractInthis paperwe answeraquestionofMikeFreedman, regardingtheeﬃciencyofpositive topological ﬁeld theories as invariants of smooth manifolds in dimensions >4. We show that simply connected closed…

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A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal…

Axiomatic TQFT, Axiomatic DQFT, and Exotic 4-Manifolds

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- 2011

In this article we prove that any unitary, axiomatic topological quantum field theory in four-dimensions can not detect changes in the smooth structure of M, a simply connected, closed (compact…

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We consider Blanchet, Habegger, Masbaum and Vogel's universal construction of topological theories in dimension two, using it to produce interesting theories that do not satisfy the usual…

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