Low-dimensional H-bordism and H-modular TQFTs

Abstract: Let H denote a class of manifolds (such as SO (oriented), O (unoriented), Spin, Pin+, Pin-, manifolds with spin defects, etc.). We define a 2+1-dimensional H-modular TQFT to be one which lives on the boundary of a bordism-invariant 3+1-dimensional H-TQFT. Correspondingly, we define a H-modular tensor category to be a H-premodular category which leads to a bordism-invariant 3+1-dimensional TQFT. When H = SO, this reproduces the familiar Witten-Reshetikhin-Turaev TQFTs and corresponding modular tensor categories. For other examples of H, non-zero H-bordism groups in dimensions 4 or lower lead to interesting complications (anomalies, mapping class group extensions, obstructions to defining the H-modular theory on all H-manifolds).

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

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Topological Quantum Field Theory Club (IST, Lisbon)

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