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Diffeomorphisms of the 4-sphere, Cerf theory and Montesinos twins

https://doi.org/10.2140/agt.2025.25.2817

Gay, David T (January 2025, Algebraic & Geometric Topology)

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Constructing Lagrangians from triple grid diagrams

https://doi.org/10.4310/JSG.250710023031

Blackwell, Sarah; Gay, David; Lambert-Cole, Peter (January 2025, Journal of Symplectic Geometry)

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Relations amongst twists along Montesinos twins in the 4-sphere

https://doi.org/10.2140/agt.2025.25.287

Gay, David T; Hartman, Daniel (January 2025, Algebraic & Geometric Topology)

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Doubly pointed trisection diagrams and surgery on 2-knots

https://doi.org/10.1017/S0305004121000165

GAY, DAVID; MEIER, JEFFREY (January 2022, Mathematical Proceedings of the Cambridge Philosophical Society)

Abstract We study embedded spheres in 4–manifolds (2–knots) via doubly pointed trisection diagrams, showing that such descriptions are unique up to stabilisation 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 (±4)–rational blowdown, and we illustrate our techniques and results with many examples.
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