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This research demonstrates non-factorizable ribbon Hopf algebras, revealing invariants in 4-dimensional handlebodies, suggesting new avenues for algebraic topology.
Building on the work of Nenciu we provide examples of non-factorizable ribbon Hopf algebras, and introduce a stronger notion of non-factorizability. These algebras are designed to provide invariants of 4-dimensional 2-handlebodies up to 2-deformations. We prove that some of the invariants derived from these examples are invariants dependent only on the boundary or on the presentation of the fundamental group of the 2-handlebody.
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Faes et al. (2026) studied this question.
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