Invariants of links and 3-manifolds obtained from Hopf algebras. (English) Zbl 0882.57002

Hennings, Mark

J. Lond. Math. Soc., II. Ser. 54, No. 3, 594-624 (1996).

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)

Keywords:

link; 3-manifold; ribbon Hopf algebra; invariants of links; invariants of 3-manifolds; colored framed links; trace functionals