Symplectic 4-manifolds admit Weinstein trisections

Abstract

We prove that every symplectic 4-manifold admits a trisection that is compatible with the symplectic structure in the sense that the symplectic form induces a Weinstein structure on each of the three sectors of the trisection. Along the way, we show that a (potentially singular) symplectic braided surface in ${\mathbb{CP}}^2$ can be symplectically isotoped into bridge position.

34 pages, 11 figures. v3 is the final draft which has been accepted for publication in J. Topology, v3 includes many improvements and corrections thanks to the anonymous referee, most noticeably an expansion of section 5, specifically Lemma 5.7

References in corpus (1)

• Bridge trisections in ${\mathbb{CP}}^2$ and the Thom conjecture (with Corrigendum)

Cited by in corpus (1)

• Bounding the Kirby-Thompson invariant of spun knots