Given two 4-dimensional ellipsoids whose symplectic sizes satisfy a specified inequality, we prove that a certain loop of symplectic embeddings between the two ellipsoids is noncontractible. The statement about symplectic ellipsoids is a particular case of a more general result. Given two convex toric domains whose first and second ECH capacities satisfy a specified inequality, we prove that a certain loop of symplectic embeddings between the two convex toric domains is noncontractible. We show how the constructed loops become contractible if the target domain becomes large enough. The proof involves studying certain moduli spaces of holomorphic cylinders in families of symplectic cobordisms arising from families of symplectic embeddings.

中文翻译：

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凸复曲面域之间辛嵌入的不可收缩循环

给定两个辛大小满足指定不等式的 4 维椭球，我们证明了两个椭球之间的某个辛嵌入循环是不可收缩的。关于辛椭球的陈述是一个更一般结果的特例。给定两个凸复曲面域，其第一和第二 ECH 容量满足指定的不等式，我们证明两个凸复曲面域之间的某个辛嵌入循环是不可收缩的。我们展示了如果目标域变得足够大，构建的循环如何变得可收缩。证明涉及研究由辛嵌入族产生的辛协边族中全纯圆柱的某些模空间。