Positivity of topological field theories in dimension at least 5

@article{Kreck2008PositivityOT,
  title={Positivity of topological field theories in dimension at least 5},
  author={Matthias Kreck and Peter Teichner},
  journal={Journal of Topology},
  year={2008},
  volume={1}
}
In this paper we answer a question of Mike Freedman, regarding the efficiency of positive topological field theories as invariants of smooth manifolds in dimensions greater than 4. We show that simply connected closed 5‐manifolds can be distinguished by such invariants. Using Barden's classification, this follows from our result which says that homology groups and the vanishing of cohomology operations with finite coefficients are detected by positive topological field theories. Moreover, we… 
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