Acta Mathematica Vietnamica

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Non Semi-Simple sl(2) Quantum Invariants, Spin Case
Christian Blanchet, Francesco Costantino, Nathan Geer, Bertrand Patureau-Mirand

 

Abstract

Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in Costantino et al. (To appear in J. Topology. arXiv:1202.3553). In their construction, the quantum parameter q is a root of unity of order 2r where r>1 is odd or congruent to 2 modulo 4. In this paper, we consider the remaining cases where r is congruent to zero modulo 4 and produce invariants of 3-manifolds with colored links, equipped with generalized spin structure. For a given 3-manifold M, the relevant generalized spin structures are (non canonically) parametrized by H1(M;C/2Z) .

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