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

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

2011-07-09

arxiv.org/abs/1107.1822v2

Mathematics

Algebraic Topology

28 pages, 21 figures

Scientific paper

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

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