Trisecting 4manifolds
Abstract
We show that any smooth, closed, oriented, connected 4manifold can be trisected into three copies of $\natural^k (S^1 \times B^3)$, intersecting pairwise in 3dimensional handlebodies, with triple intersection a closed 2dimensional 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 3manifolds. A trisection of a 4manifold $X$ arises from a Morse 2function $G:X \to B^2$ and the obvious trisection of $B^2$, in much the same way that a Heegaard splitting of a 3manifold $Y$ arises from a Morse function $g : Y \to B^1$ and the obvious bisection of $B^1$.
 Publication:

arXiv eprints
 Pub Date:
 May 2012
 arXiv:
 arXiv:1205.1565
 Bibcode:
 2012arXiv1205.1565G
 Keywords:

 Mathematics  Geometric Topology;
 57M99 (Primary) 57R45 (Secondary)
 EPrint:
 38 pages, 29 figures