• Corpus ID: 36079049

Positive topological field theories and manifolds of dimension 5

@inproceedings{Kreck2007PositiveTF,
  title={Positive topological field theories and manifolds of dimension 5},
  author={Matthias Kreck and Peter Teichner},
  year={2007}
}

• M. Kreck, P. Teichner
• Published 2007
• Mathematics

AbstractInthis paperwe answeraquestionofMikeFreedman, regardingtheefficiencyofpositive topological field theories as invariants of smooth manifolds in dimensions >4. We show that simply connected closed 5-manifolds can be distinguished bysuch invariants. Using Barden’s classification, this follows from our observationthat homology groups and the vanishing of cohomology operations with finitecoefficients are detected by positive topological field theories. Moreover, we provethat in the non-simply connected case, as well as in all dimensions d>5, theuniversal manifold pairing (and in particular, d-dimensional positive topologicalfield theories) are not sufficient to distinguish compact d-manifolds with boundaryS 3 × S n ,n > 1 and S 4k−1 ,k > 1. The latter case is equivalent to the samestatement for closed 4k-manifolds. 1 Introduction In [FKNSWW] the authors study the universal manifold pairing related to positiveunitary topological quantum field theories, in short PTFT’s, see Definition 4. Theyshow that closed smooth oriented manifolds of dimension ≤ 2 can be detected byPTFT’s. Moreover, they prove that in dimension 4 two s-cobordant manifolds,with small 4-balls removed, represent the same vector in the universal vector space