$T^3$-fibrations on compact six-manifolds

Details $T^3$-fibrations on compact six-manifolds $T^3$-fibrations on compact six-manifolds

2001-09-13

arxiv.org/abs/math/0109087v1

Mathematics

Differential Geometry

32 pages, 2 figures

Scientific paper

We describe a simple way of constructing torus fibrations $T^3\to X\to S^3$ which degenerate canonically over a knot or link in $S^3$. 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 $T^3$-fibrations $S^3\times S^3\to S^3$ and $(S^3\times S^3)#(S^3\times S^3)#(S^4\times S^2) \to S^3$ whose discriminant locus is a torus knot.

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