We study relative symplectic cobordisms between contact submanifolds, and in particular relative symplectic cobordisms to the empty set, that we call hats. While we make some observations in higher dimensions, we focus on the case of transverse knots in the standard 3-sphere, and hats in blow-ups of the (punctured) complex projective planes. We apply the construction to give constraints on the algebraic topology of fillings of double covers of the 3-sphere branched over certain transverse quasipositive knots.

中文翻译：

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辛帽子

我们研究了接触子流形之间的相对辛协边，特别是空集的相对辛协边，我们称之为帽子。虽然我们在更高维度上进行了一些观察，但我们专注于标准 3 球体中的横向结的情况，以及（刺穿的）复杂投影平面爆炸中的帽子。我们应用该构造来限制在某些横向准正结上分支的三球体的双覆盖的填充的代数拓扑。