Kirby elements and quantum invariants

• Autores: Alexis Virelizier
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 93, Nº 2, 2006, págs. 474-514
• Idioma: inglés
• DOI: 10.1112/s0024611506015905
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• Resumen

  • We define the notion of a Kirby element of a ribbon category $\mathcal{C}$ (not necessarily semisimple). Kirby elements lead to 3-manifold invariants. We characterize a class of Kirby elements, the algebraic Kirby elements, in terms of the structure maps of a Hopf algebra in $\mathcal{C}$. This class is sufficiently large to recover the quantum invariants of 3-manifolds of Reshetikhin and Turaev, of Hennings, Kauffman and Radford, and of Lyubashenko when these are well defined. The cases of a semisimple ribbon category and of a category of representations are explored in detail.