Non semi-simple \({\mathfrak {sl}(2)}\) quantum invariants, spin case.(English)Zbl 1345.57019
F. Costantino et al. [J. Topol. 7, No. 4, 1005–1053 (2014;Zbl 1320.57016)] constructed invariants of 3-manifolds equipped with a 1-dimensional cohomology class over \(\mathbb{C}/2\mathbb{Z}\), using a non semi-simple representation category of quantum \(\mathfrak{sl}(2)\) with quantum parameter \(q\) a root of unity of order \(2r\) with \(r>1,r\not\equiv0\pmod{4}\).
In the paper under review, the authors consider the case \(r\equiv0\pmod4\). They obtain invariants for 3-manifolds with a kind of generalized spin structures. The generalized spin structure for a 3-manifold \(M\) is non-canonically parametrized by \(H^1(M; \mathbb{C}/2\mathbb{Z})\).
In the paper under review, the authors consider the case \(r\equiv0\pmod4\). They obtain invariants for 3-manifolds with a kind of generalized spin structures. The generalized spin structure for a 3-manifold \(M\) is non-canonically parametrized by \(H^1(M; \mathbb{C}/2\mathbb{Z})\).
Reviewer: Kazuo Habiro (Kyoto)
MSC:
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
Citations:
Zbl 1320.57016Cite
References:
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