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

TL;DR

This paper presents a new method for constructing torus fibrations on compact six-manifolds with degenerations over knots or links, and computes their topological invariants algebraically, leading to novel examples with torus knot discriminant loci.

Contribution

It introduces a simple construction technique for $T^3$-fibrations on six-manifolds with degenerations over knots or links, and provides algebraic methods to compute their invariants.

Findings

Constructed new $T^3$-fibrations on specific six-manifolds.

Computed topological invariants algebraically from monodromy.

Produced examples with discriminant loci as torus knots.

Abstract

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.