Trisections of Lefschetz Pencils
Abstract
Donaldson showed that every closed symplectic 4manifold can be given the structure of a topological Lefschetz pencil. Gay and Kirby showed that every closed 4manifold 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 4dimensional analog of the following trivial 3dimensional result: For every open book decomposition of a 3manifold M, there is a decomposition of M into three handlebodies, each of which is a regular neighborhood of a page.
 Publication:

arXiv eprints
 Pub Date:
 October 2015
 arXiv:
 arXiv:1510.08791
 Bibcode:
 2015arXiv151008791G
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Symplectic Geometry;
 57M99 (Primary);
 57R17 (Secondary)
 EPrint:
 9 pages, 9 figures