Trisecting 4–manifolds

Gay, David¹ ; Kirby, Robion²

¹ Euclid Lab, 160 Milledge Terrace, Athens, GA 30606, United States, Department of Mathematics, University of Georgia, Athens, GA 30602, United States
² Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720-3840, United States

Geometry & topology, Tome 20 (2016) no. 6, pp. 3097-3132.

Résumé

We show that any smooth, closed, oriented, connected $4$–manifold can be trisected into three copies of ${♮}^k\left(S^1\times B^3\right)$, intersecting pairwise in $3$–dimensional handlebodies, with triple intersection a closed $2$–dimensional surface. Such a trisection is unique up to a natural stabilization operation. This is analogous to the existence, and uniqueness up to stabilization, of Heegaard splittings of $3$–manifolds. A trisection of a $4$–manifold $X$ arises from a Morse $2$–function $G:X\to B^2$ and the obvious trisection of $B^2$, in much the same way that a Heegaard splitting of a $3$–manifold $Y$ arises from a Morse function $g:Y\to B^1$ and the obvious bisection of $B^1$.

Détail

DOI : 10.2140/gt.2016.20.3097

Classification : 57M50, 57M99, 57R45, 57R65
Keywords: 4-manifold, trisection, Heegaard splitting, Heegaard triple, Morse 2-function

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