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Invariants of links and 3-manifolds obtained from Hopf algebras. (English) Zbl 0882.57002
N. Y. Reshetikhin and V. G. Turaev [Commun. Math. Phys. 127, No. 1, 1-26 (1990; Zbl 0768.57003)] and S. Majid [Int. J. Mod. Phys. A 5, No. 1, 1-91 (1990; Zbl 0709.17009)] used representations of a quasitriangular ribbon Hopf algebra to construct invariants of colored framed links. Then taking linear combinations of them, invariants for $$3$$-manifolds were obtained [N. Y. Reshetikhin and V. G. Turaev, Invent. Math. 103, No. 3, 547-597 (1991; Zbl 0725.57007)]. In this paper under review, the author finds more general sufficient conditions to define invariants of $$3$$-manifolds, using trace functionals rather than representations.
Reviewer: H.Murakami (Tokyo)

MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010) 57N10 Topology of general $$3$$-manifolds (MSC2010)
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