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A finite set of generators for the Kauffman bracket skein algebra. (English) Zbl 0932.57016

Summary: If \(F\) is a compact orientable surface it is known that the Kauffman bracket skein module of \(F\times I\) has a multiplicative structure. Our central result is the construction of a finite set of knots which generate the module as an algebra. We can then define an integer valued invariant of compact orientable 3-manifolds which characterizes \(S^3\).

MSC:

57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57N10 Topology of general \(3\)-manifolds (MSC2010)
57M99 General low-dimensional topology
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57N12 Topology of the Euclidean \(3\)-space and the \(3\)-sphere (MSC2010)
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