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Acta Mathematica Vietnamica

, Volume 39, Issue 4, pp 481–495 | Cite as

Non Semi-Simple \({\mathfrak {sl}(2)}\) Quantum Invariants, Spin Case

  • Christian Blanchet
  • Francesco Costantino
  • Nathan Geer
  • Bertrand Patureau-Mirand
Article
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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 \(H^{1}(M;\mathbb{C}/2\mathbb{Z})\).

Keywords

Quantum invariants 3-manifolds Non semi-simple Spin structures 

Mathematics Subject Classification (2010)

57M27 

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2014

Authors and Affiliations

  • Christian Blanchet
    • 1
  • Francesco Costantino
    • 2
  • Nathan Geer
    • 3
  • Bertrand Patureau-Mirand
    • 4
  1. 1.IMJ-PRG, UMR 7586 CNRS, Univ Paris Diderot, Sorbonne Paris CitéUniv Paris DiderotParisFrance
  2. 2.Institut de Mathématiques de Toulouse (IMT)Université de Toulouse III Paul SabatierToulouseFrance
  3. 3.Mathematics and StatisticsUtah State UniversityLoganUSA
  4. 4.Univ. Bretagne - Sud, UMR 6205, LMBAVannesFrance

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