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Much work has been done on the existence and uniqueness of broken Lefschetzfibrations such as those by Auroux et al., Gay and Kirby, Lekili, Akbulut andKarakurt, Baykur, and Williams, but there has been a lack of explicit examples.A theorem of Gay and Kirby suggests the existence of a broken Lefschetzfibration of S^4 over S^2 with a 2-knot fiber. In the case of a spun ortwist-spun torus knot, we present a procedure to construct such fibrationsexplicitly. The fibrations constructed have no cusps nor Lefschetzsingularities.

Constructing a broken Lefschetz fibration of S^4 with a spun or twist-spun torus knot fiber