Doubly pointed trisection diagrams and surgery on 2-knots

David Gay; Jeffrey Meier

doi:10.1017/s0305004121000165

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arXiv · 1806.05351

Doubly pointed trisection diagrams and surgery on 2-knots

David Gay·Jeffrey Meier

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Abstract

We study embedded spheres in 4-manifolds (2-knots) via doubly pointed trisection diagrams, showing that such descriptions are unique up to stabilization and handleslides, and we describe how to obtain trisection diagrams for certain cut-and-paste operations along 2-knots directly from doubly pointed trisection diagrams. The operations described are classical surgery, Gluck surgery, blowdown, and $(\pm4)$-rational blowdown, and we illustrate our techniques and results with many examples.

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David Gay, Jeffrey Meier. 2018-06-14. Doubly pointed trisection diagrams and surgery on 2-knots. https://doi.org/10.1017/s0305004121000165

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