A direct construction produces PALFs with genus at most (N-1)/2 from 2-handle decompositions of Stein surfaces and bounds the minimal genus invariant for knot traces by the same quantity.
[Uki] Takuya Ukida,Small genus positive allowable Lefschetz fibrations on compact Stein 4-manifolds, in preparation
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A Simple Construction of Lefschetz Fibrations on Compact Stein Surfaces
A direct construction produces PALFs with genus at most (N-1)/2 from 2-handle decompositions of Stein surfaces and bounds the minimal genus invariant for knot traces by the same quantity.