Given a manifold M with a submanifold N, the deformation space D(M,N) is a manifold with a submersion to R whose zero fiber is the normal bundle, and all other fibers are equal to M. This article uses deformation spaces to study the local behavior of various geometric structures associated with singular foliations, with N a submanifold transverse to the foliation. New examples include L_\infty-algebroids, Courant algebroids, and Lie bialgebroids. In each case, we obtain a normal form theorem around N, in terms of a model structure over the normal bundle.

中文翻译：

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横截面周围的变形空间和正常形式

给定一个带有子流形N的流形M，变形空间D(M,N)是一个浸没到R的流形，其零纤维为法丛，其他所有纤维都等于M。 本文使用变形空间来研究与奇异叶理相关的各种几何结构的局部行为，其中 N 是横向于叶理的子流形。新的例子包括 L_\infty-algebroids、Courant algebroids 和 Lie bialgebroids。在每种情况下，我们都根据法丛上的模型结构获得了围绕 N 的范式定理。