拉格朗日吹胀、吹胀及在实际包装中的应用
Lagrangian blow-ups, blow-downs, and applications to real packing
摘要：
给定一个辛流形（M，ω）和一个拉格朗日子流形L，我们构造了相对于L定义的辛blow-up和blow-down形式.进一步证明了，如果M允许一个反辛对合，并且我们对辛球的一个适当对称嵌入进行爆破，那么在爆破上也存在一个反辛对合.我们导出了一个同调条件，它决定了当一个实Lagrange曲面L = Fix（n）的拓扑在一次吹落后何时发生变化，并利用这些构造研究了非Seiberg-Witten单的实秩1辛四流形的实堆积数和填充稳定性.
英文摘要：
Given a symplectic manifold (M, ω) and a Lagrangian submanifold L, we construct versions of the symplectic blow-up and blow-down which are defined relative to L. Furthermore, we show that if M admits an anti-symplectic involution ϕ and we blow-up an appropriately symmetric embedding of symplectic balls, then there exists an anti-symplectic involution on the blow-up as well. We derive a homological condition which determines when the topology of a real Lagrangian surface L = Fix(ϕ) changes after a blow down, and we use these constructions to study the real packing numbers and packing stability for real, rank-1 symplectic four manifolds which are non-Seiberg-Witten simple.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
