From Heegaard splittings to trisections; porting 3-dimensional ideas to dimension 4

David T. Gay

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arXiv · 1902.01797

From Heegaard splittings to trisections; porting 3-dimensional ideas to dimension 4

David T. Gay

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Abstract

These notes summarize and expand on a mini-course given at CIRM in February 2018 as part of Winter Braids VIII. We somewhat obsessively develop the slogan `Trisections are to 4-manifolds as Heegaard splittings are to 3-manifolds', focusing on and clarifying the distinction between three ways of thinking of things: the basic definitions as decompositions of manifolds, the Morse theoretic perspective and descriptions in terms of diagrams. We also lay out these themes in two important relative settings: 4-manifolds with boundary and 4-manifolds with embedded 2-dimensional submanifolds.

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David T. Gay. 2019-02-05. From Heegaard splittings to trisections; porting 3-dimensional ideas to dimension 4. https://arxiv.org/abs/1902.01797

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