Symplectic 4-manifolds admit Weinstein trisections

摘要

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 CP2 can be symplectically isotoped into bridge position. This paper relies extensively on colour figures. Some references to colour may not be meaningful in the printed version, and we refer the reader to the online version which includes the colour figures.