2018/07/31 by Francis Bischoff, Henrique Bursztyn, Hudson Lima +1 · 1 citation
Mathematics · #math.DG #math.SG
paper · pdf · doi:10.1112/s0010437x1900784x
published as Compositio Math. 156 (2020) 697-732 · 36 pages. v2: typos fixed
arxiv created 2018/08/13 · arxiv updated 2020/02/19
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_∞-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.