Trisecting $4$–manifolds

@inproceedings{Gay2016Trisecting,
  title={Trisecting \$4\$–manifolds},
  author={David T. Gay and Robion C. Kirby},
  year={2016}
}
We show that any smooth, closed, oriented, connected 4‐manifold can be trisected into three copies of \ k .S 1 B 3 /, 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 GW X! B 2 and the obvious… CONTINUE READING

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