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2016 Trisections of Lefschetz pencils
David Gay
Algebr. Geom. Topol. 16(6): 3523-3531 (2016). DOI: 10.2140/agt.2016.16.3523


Donaldson [J. Differential Geom. 53 (1999) 205–236] showed that every closed symplectic 4–manifold can be given the structure of a topological Lefschetz pencil. Gay and Kirby [Geom. Topol. 20 (2016) 3097–3132] showed that every closed 4–manifold has a trisection. In this paper we relate these two structure theorems, showing how to construct a trisection directly from a topological Lefschetz pencil. This trisection is such that each of the three sectors is a regular neighborhood of a regular fiber of the pencil. This is a 4–dimensional analog of the following trivial 3–dimensional result: for every open book decomposition of a 3–manifold M, there is a decomposition of M into three handlebodies, each of which is a regular neighborhood of a page.


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David Gay. "Trisections of Lefschetz pencils." Algebr. Geom. Topol. 16 (6) 3523 - 3531, 2016.


Received: 30 October 2015; Revised: 10 May 2016; Accepted: 19 May 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1375.57023
MathSciNet: MR3584265
Digital Object Identifier: 10.2140/agt.2016.16.3523

Primary: 57M50, 57M99
Secondary: 57R17, 57R45, 57R65

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 6 • 2016
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