| Résume | Abstract: I will present some of the results contained in the paper Quantum Invariants of 3-Manifolds via Link Surgery Presentations and Non-Semi-Simple Categories by Costantino, Geer and Patureau. We will construct two families of invariants of closed 3-manifolds indexed by a natural parameter r>1. These invariants are built out of the non-semisimple category of representations of the unrolled quantum group U_q^H(sl_2) at a 2r-th root of unity we saw in the first talk. The secondary invariants conjecturally extend the original Reshetikhin-Turaev invariants for the small quantum group \barU_q(sl_2). The use of richer categories pays off as these non-semisimple invariants are strictly finer than the original semisimple ones: indeed they can be used to recover the classification of lens spaces, which Reshetikhin-Turaev invariants could not always distinguish.
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[Page du GDT->http://webusers.imj-prg.fr/~marco.de-renzi/gdt.htm] |
