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3-dimensional defect TQFTs and their tricategories
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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 the natural categorification of a pivotal bicategory. This captures the algebraic essence of defect TQFTs, and it gives precise meaning to the fusion of line and surface defects as well as their duality operations. As examples, we discuss how Reshetikhin-Turaev and Turaev-Viro theories embed into our framework, and how they can be extended to defect TQFTs.
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Topological defects in reflection positive topological field theories
A reflection-positive two-dimensional defect TQFT gives its defect bicategory an O(2)-dagger structure, and with positivity a structure close to a 3-Hilbert space.
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