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Deformation spaces and normal forms around transversals

  • Francis Bischoff (a1), Henrique Bursztyn (a2), Hudson Lima (a3) and Eckhard Meinrenken (a4)

Abstract

Given a manifold $M$ with a submanifold $N$ , the deformation space ${\mathcal{D}}(M,N)$ is a manifold with a submersion to $\mathbb{R}$ whose zero fiber is the normal bundle $\unicode[STIX]{x1D708}(M,N)$ , 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 $\unicode[STIX]{x1D708}(M,N)$ .

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Deformation spaces and normal forms around transversals

  • Francis Bischoff (a1), Henrique Bursztyn (a2), Hudson Lima (a3) and Eckhard Meinrenken (a4)

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