Defines defect skein modules for 3-manifolds with line and point defects and proves they match state spaces of defect Reshetikhin-Turaev TQFT for semisimple data.
The blob complex
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abstract
Given an n-manifold M and an n-category C, we define a chain complex (the "blob complex") B_*(M;C). The blob complex can be thought of as a derived category analogue of the Hilbert space of a TQFT, and as a generalization of Hochschild homology to n-categories and n-manifolds. It enjoys a number of nice formal properties, including a higher dimensional generalization of Deligne's conjecture about the action of the little disks operad on Hochschild cochains. Along the way, we give a definition of a weak n-category with strong duality which is particularly well suited for work with TQFTs.
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math.QA 1years
2026 1verdicts
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Defects in skein theory and TQFT
Defines defect skein modules for 3-manifolds with line and point defects and proves they match state spaces of defect Reshetikhin-Turaev TQFT for semisimple data.