From Heegaard splittings to trisections; porting 3-dimensional ideas to dimension 4
David T Gay1
1 Euclid Lab 160 Milledge Terrace Athens, GA 30606 Department of Mathematics University of Georgia Athens, GA 30602
Winter Braids Lecture Notes, Volume 5 (2018), Talk no. 4, 19 p.

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.

Published online:
DOI: 10.5802/wbln.24
David T Gay 1

1 Euclid Lab 160 Milledge Terrace Athens, GA 30606 Department of Mathematics University of Georgia Athens, GA 30602 
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David T Gay. From Heegaard splittings to trisections; porting $3$-dimensional ideas to dimension $4$. Winter Braids Lecture Notes, Volume 5 (2018), Talk no. 4, 19 p. doi : 10.5802/wbln.24. https://proceedings.centre-mersenne.org/articles/10.5802/wbln.24/

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