Kirby elements and quantum invariants

Alexis Virelizier

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arXiv · math/0312337

Kirby elements and quantum invariants

Alexis Virelizier

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Abstract

We define the notion of a Kirby element of a ribbon category C (not necessarily semisimple). Kirby elements lead to 3-manifolds invariants. We characterize (in terms of the structure maps of some categorical Hopf algebra) a set of Kirby elements of C which is sufficiently large to recover the known quantum invariants computed from C. The cases of a semisimple ribbon category and of a category of representations are explored in details.

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Alexis Virelizier. 2003-12-17. Kirby elements and quantum invariants. https://arxiv.org/abs/math/0312337

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