Depicting a Generalized Shift Move in Crown Diagrams
Keywords:
crown diagram, 4-manifold, Lefschetz fibrationAbstract
We give a diagrammatic way to perform a generalized shift move on a crown diagram of a smooth 4 -manifold. Applications include a simplified proof that if two crown diagrams are related by a generalized shift move, then they are slide-equivalent; a method for converting a genus $g>1$ Lefschetz fibration into a crown diagram; and a proof that the vanishing cycles of such a crown diagram are slide-equivalent to a standard inclusion of the Lefschetz vanishing cycles into a genus $g+1$ surface.
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