T³-fibrations on compact six-manifolds

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We describe a simple way of constructing torus fibrations T³→ X→ S³ which degenerate canonically over a knot or link in S³. We show that the topological invariants of X can be computed algebraically from the monodromy representation of the fibration. We use this to obtain some new T³-fibrations S³× S³→ S³ and (S³× S³)#(S³× S³)#(S⁴× S²) → S³ whose discriminant locus is a torus knot.