Manifold calculus is a form of functor calculus that analyzes contravariant functors from some categories of manifolds to topological spaces by providing analytic approximations to them. In this paper, using the technique of the h-principle, we show that for a symplectic manifold N, the analytic approximation to the Lagrangian embeddings functor \(\mathrm {Emb}_{\mathrm {Lag}}(-,N)\) is the totally real embeddings functor \(\mathrm {Emb}_{\mathrm {TR}}(-,N)\). More generally, for subsets \({\mathcal {A}}\) of the m-plane Grassmannian bundle \({{\,\mathrm{{Gr}}\,}}(m,TN)\) for which the h-principle holds for \({\mathcal {A}}\)-directed embeddings, we prove the analyticity of the \({\mathcal {A}}\)-directed embeddings functor \({{\,\mathrm{Emb}\,}}_{{\mathcal {A}}}(-,N)\).

中文翻译：

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h原理在流形微积分中的应用

流形微积分是函子微积分的一种形式，它通过提供对它们的解析逼近来分析从某些类型的流形到拓扑空间的互变量。在本文中，使用h原理的技术，我们证明对于辛流形N，对Lagrangian嵌入函子\（\ mathrm {Emb} _ {\ mathrm {Lag}}（-，N）的解析近似\）是完全真实的嵌入函子\（\ mathrm {Emb} _ {\ mathrm {TR}}（-，N）\）。更一般地，对于子集\（{\ mathcal {A}} \）的米-平面格拉斯曼管束\（{{\，\ mathrm {{的Gr}} \，}}（米，TN）\）的量，H- （\（{\ mathcal {A}} \）定向嵌入的原理成立，我们证明了\（{\ mathcal {A}} \\）定向嵌入函子\（{{\，\ mathrm {Emb } \，}} _ {{\数学{A}}}（-，N）\）。