Positive topological quantum field theories

  • Markus Banagl

    Universität Heidelberg, Germany


We propose a new notion of positivity for topological field theories (TFTs), based on S. Eilenberg’s concept of completeness for semirings. We show that a complete ground semiring, a system of fields on manifolds and a system of action functionals on these fields determine a positive TFT. The main feature of such a theory is a semiring-valued topologically invariant state sum that satisfies a gluing formula. The abstract framework has been carefully designed to cover a wide range of phenomena. We indicate how to employ the framework presented here in constructing a new differential topological invariant that detects exotic smooth structures on spheres.

Cite this article

Markus Banagl, Positive topological quantum field theories. Quantum Topol. 6 (2015), no. 4, pp. 609–706

DOI 10.4171/QT/71