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Formal rigidity of singular foliations around fixed points

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Karandeep Singh
Mit, 08/11/2023 - 10:30 - 12:00
MPIM Seminar Room

In mathematics, rigidity questions arise in various settings. For instance, given a Lie algebra structure $\mu$ on a finite-dimensional vector space $V$, seen as a bilinear map, it is natural to ask when all nearby Lie algebra structures are related to $\mu$ by a linear automorphism of $V$. In geometry, similar questions arise when dealing with Lie algebra actions or Poisson structures, for which various results have been obtained. I will discuss the rigidity question for singular foliations, and show that analytic foliations are formally rigid around fixed points with semisimple isotropy Lie algebra, using Lie $n$-algebroids.

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