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We specialise the construction of orbifold graph TQFTs introduced in Carqueville et al., arXiv:2101.02482 to Reshetikhin-Turaev defect TQFTs. We explain that the modular fusion category ${mathcal{C}}_{mathcal{A}}$ constructed in Muleviv{c}ius-Runkel, arXiv:2002.00663 from an orbifold datum $mathcal{A}$ in a given modular fusion category $mathcal{C}$ is a special case of the Wilson line ribbon categories introduced as part of the general theory of orbifold graph TQFTs. Using this, we prove that the Reshetikhin-Turaev TQFT obtained from ${mathcal{C}}_{mathcal{A}}$ is equivalent to the orbifold of the TQFT for $mathcal{C}$ with respect to the orbifold datum $mathcal{A}$.
We introduce the notion of $n$-dimensional topological quantum field theory (TQFT) with defects as a symmetric monoidal functor on decorated stratified bordisms of dimension $n$. The familiar closed or open-closed TQFTs are special cases of defect TQ
A generalised orbifold of a defect TQFT $mathcal{Z}$ is another TQFT $mathcal{Z}_{mathcal{A}}$ obtained by performing a state sum construction internal to $mathcal{Z}$. As an input it needs a so-called orbifold datum $mathcal{A}$ which is used to lab
We prove the $r$-spin cobordism hypothesis in the setting of (weak) 2-categories for every positive integer $r$: The 2-groupoid of 2-dimensional fully extended $r$-spin TQFTs with given target is equivalent to the homotopy fixed points of an induced
We initiate a systematic study of 3-dimensional `defect topological quantum field theories, that we introduce as symmetric monoidal functors on stratified and decorated bordisms. For every such functor we construct a tricategory with duals, which is
We identify the leading order term of the asymptotic expansion of the Witten-Reshetikhin-Turaev invariants for finite order mapping tori with classical invariants for all simple and simply-connected compact Lie groups. The square root of the Reidemei