In this paper, we construct invariants of 3-manifolds 'A la Reshetikhin-Turaev ' in the setting of non-semi-simple ribbon tensor categories. We give concrete examples of such categories that lead to a family of 3-manifold invariants indexed by the integers. We prove that this family of invariants has several notable features, including: they can be computed via a set of axioms, they distinguish homotopically equivalent manifolds that THE standard Witten-Reshetikhin-Turaev invariants do not and they allow the statement of a version of the Volume Conjecture and a proof of this conjecture for an infinite class of links.
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机译：在本文中，我们在非半简单带张量类别的背景下构造了3个流形“ A la Reshetikhin-Turaev”的不变量。我们给出此类类别的具体示例，这些类别会导致一个由整数索引的3流形不变量。我们证明了这一不变量家族具有几个显着特征，包括：可以通过一组公理来计算，它们区分标准Witten-Reshetikhin-Turaev不变量所不具有的同位等价流形，并且它们允许使用体积猜想以及对无限类链接的这种猜想的证明。
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