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. 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.

中文翻译：

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辛四流形承认温斯坦三等分

我们证明，每个辛四流形都接受一个与辛结构相容的三等分，就这一意义而言，辛形式在三等分的三个部分中的每一个上都诱发了韦恩斯坦结构。一路走来，我们证明了一个（可能是奇异的）辛编织表面${\mathbb{CP}}^{\mathrm{2个}}$可以折衷地同位素化到桥的位置 本文广泛地依赖于彩色图形。对颜色的某些引用在印刷版本中可能没有意义，我们请读者阅读包含颜色数字的在线版本。