Abstract
Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum \({\mathfrak {sl}(2)}\) 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 \(H^{1}(M;\mathbb{C}/2\mathbb{Z})\).
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Blanchet, C., Costantino, F., Geer, N. et al. Non Semi-Simple \({\mathfrak {sl}(2)}\) Quantum Invariants, Spin Case. Acta Math Vietnam 39, 481–495 (2014). https://doi.org/10.1007/s40306-014-0089-5
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DOI: https://doi.org/10.1007/s40306-014-0089-5