Pré-Publication, Document De Travail Année : 2025

Quantum Invariants of Ribbon Surfaces in 4-Dimensional 2-Handlebodies

Résumé

We use unimodular ribbon categories to construct quantum invariants of ribbon surfaces in $4$-dimensional $2$-handlebodies up to $1$-isotopy. In the process, we recover invariants due to Bobtcheva-Messia, Broda-Petit, Gainutdinov-Geer-Patureau-Runkel (in collaboration with the second author), and Lee-Yetter. Our approach does not assume semisimplicity, and is based on a generalization of the Reshetikhin-Turaev functor to the category of labeled Kirby graphs which also yields invariants of framed links in the boundary of $4$-dimensional $2$-handlebodies up to $2$-deformations. The setup is very flexible, and allows for several different constructions, using central elements satisfying equations introduced by Hennings and Bobtcheva-Messia, modified traces, and modules over Frobenius algebras satisfying conditions dictated by the diagrammatic calculus for embedded surfaces developed by Hughes, Kim, and Miller.

Dates et versions

hal-05477389 , version 1 (26-01-2026)

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Anna Beliakova, Marco De Renzi, Quentin Faes. Quantum Invariants of Ribbon Surfaces in 4-Dimensional 2-Handlebodies. 2025. ⟨hal-05477389⟩
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