Depicting a generalized shift move in crown diagrams

J Williams

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arXiv · 2202.04749

Depicting a generalized shift move in crown diagrams

J Williams

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Abstract

This paper gives 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 the fact 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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J Williams. 2022-02-09. Depicting a generalized shift move in crown diagrams. https://arxiv.org/abs/2202.04749

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