Meusburger C (2023)
Publication Type: Journal article
Publication year: 2023
Book Volume: 429
Article Number: 109177
DOI: 10.1016/j.aim.2023.109177
We define a Turaev-Viro-Barrett-Westbury state sum model of triangulated 3-manifolds with surface, line and point defects. Surface defects are oriented embedded 2d PL submanifolds and are labelled with bimodule categories over spherical fusion categories with bimodule traces. Line and point defects form directed graphs on these surfaces and labelled with bimodule functors and bimodule natural transformations. The state sum is based on generalised 6j symbols that encode the coherence isomorphisms of the defect data. We prove the triangulation independence of the state sum and show that it can be computed in terms of polygon diagrams that satisfy the cutting and gluing identities for polygon presentations of oriented surfaces. By computing state sums with defect surfaces, we show that they detect the genus of a defect surface and are sensitive to its embedding. We show that defect lines on defect surfaces with trivial defect data define ribbon invariants for the centre of the underlying spherical fusion category.
APA:
Meusburger, C. (2023). State sum models with defects based on spherical fusion categories. Advances in Mathematics, 429. https://dx.doi.org/10.1016/j.aim.2023.109177
MLA:
Meusburger, Cathérine. "State sum models with defects based on spherical fusion categories." Advances in Mathematics 429 (2023).
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