This is a mixture of survey article and research announcement. We discuss instanton Floer homology for 3 manifolds with boundary. We also discuss a categorification of the Lagrangian Floer theory using the unobstructed immersed Lagrangian correspondence as a morphism in the category of symplectic manifolds.During the year 1998–2012, those problems have been studied emphasizing the ideas from analysis such as degeneration and adiabatic limit (instanton Floer homology) and strip shrinking (Lagrangian correspondence). Recently we found that replacing those analytic approach by a combination of cobordism type argument and homological algebra, we can resolve various difficulties in the analytic approach. It thus solves various problems and also simplify many of the proofs.

中文翻译：

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规范理论和辛几何的不变量分类

这是调查文章和研究公告的混合。我们讨论了带边界的3个流形的瞬时Floer同源性。我们还将讨论Lagrangian Floer理论的分类，其中使用无障碍的沉浸式Lagrangian对应作为辛流形范畴中的变态。在1998-2012年期间，对这些问题进行了研究，着重强调了诸如退化和绝热极限（ Instanton Floer同源性）和条带收缩（拉格朗日对应）。最近，我们发现用cobordism类型的论点和同源代数的组合代替那些分析方法，可以解决分析方法中的各种困难。因此，它解决了各种问题，并且简化了许多证明。