Modified 6j-Symbols and 3-Manifold Invariants

Nathan Geer; Bertrand Patureau-Mirand; Vladimir Turaev

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arXiv · 0910.1624

Modified 6j-Symbols and 3-Manifold Invariants

Nathan Geer·Bertrand Patureau-Mirand·Vladimir Turaev

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Abstract

We show that the renormalized quantum invariants of links and graphs in the 3-sphere, derived from tensor categories in ["Modified quantum dimensions and re-normalized link invariants", arXiv:0711.4229] lead to modified 6j-symbols and to new state sum 3-manifold invariants. We give examples of categories such that the associated standard Turaev-Viro 3-manifold invariants vanish but the secondary invariants may be non-zero. The categories in these examples are pivotal categories which are neither ribbon nor semi-simple and have an infinite number of simple objects.

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Nathan Geer, Bertrand Patureau-Mirand, Vladimir Turaev. 2009-11-12. Modified 6j-Symbols and 3-Manifold Invariants. https://arxiv.org/abs/0910.1624

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