Trisecting 4–manifolds

Gay, David; Kirby, Robion

doi:10.2140/gt.2016.20.3097

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Trisecting $4$–manifolds

David T Gay and Robion Kirby

Geometry & Topology 20 (2016) 3097–3132

DOI: 10.2140/gt.2016.20.3097

Abstract

We show that any smooth, closed, oriented, connected $4$ –manifold can be trisected into three copies of $♮^{k} (S^{1} \times B^{3})$ , 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 $G : X \to B^{2}$ 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 $B^{1}$ .

Keywords

4-manifold, trisection, Heegaard splitting, Heegaard triple, Morse 2-function

Mathematical Subject Classification 2010

Primary: 57M50, 57M99

Secondary: 57R45, 57R65

References

Publication

Received: 4 December 2013

Revised: 21 January 2016

Accepted: 18 February 2016

Published: 21 December 2016

Proposed: Yasha Eliashberg

Seconded: Benson Farb, Dmitri Burago

Authors

David T Gay
Euclid Lab 160 Milledge Terrace Athens, GA 30606 United States	Department of Mathematics University of Georgia Athens, GA 30602 United States

Robion Kirby
Department of Mathematics University of California, Berkeley Berkeley, CA 94720-3840 United States

Volume 20, issue 6 (2016)