A modular tensor category gives rise to a Reshetikhin–Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded -coloured ribbon graphs. We extend this construction to include bordisms with surface defects which in turn can meet along line defects. The surface defects are labelled by -separable symmetric Frobenius algebras and the line defects by “multi-modules” which are equivariant with respect to a cyclic group action. Our invariant cannot distinguish non-isotopic embeddings of 2-spheres, but we give an example where it distinguishes non-isotopic embeddings of 2-tori.
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Nils Carqueville, Ingo Runkel, Gregor Schaumann, Line and surface defects in Reshetikhin–Turaev TQFT. Quantum Topol. 10 (2019), no. 3, pp. 399–439DOI 10.4171/QT/121