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Non Semi-Simple $sl (2)$ Quantum Invariants, Spin Case

$icon-email$ 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 $2 r$ 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 $H^{1} (M; C / 2 Z)$ .

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Non Semi-Simple sl(2) Quantum Invariants, Spin Case

Abstract

Non Semi-Simple $sl (2)$ Quantum Invariants, Spin Case