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GENERALIZED FLOW-BOX PROPERTY FOR SINGULAR FOLIATIONS

Abstract : We introduce a notion of generalized Flow-Box property valid for general singular distributions and sub-varieties (based on a dynamical interpretation). Just as in the usual Flow-Box Theorem, we characterize geometrical and algebraic conditions of (quasi) transversality in order for an analytic sub-variety X (not necessarily regular) to be a section of a line foliation. We also discuss the case of more general foliations. This study is originally motivated by a question of Jean-François Mattei (Invent Math 103(2):297–325, 1991, Theorem 3.2.1) about the existence of local slices for a (non-compact) Lie group action.
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Submitted on : Monday, July 27, 2020 - 11:59:38 AM
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Andre Belotto da Silva, Daniel Panazzolo. GENERALIZED FLOW-BOX PROPERTY FOR SINGULAR FOLIATIONS. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales - Serie A. Matemáticas, Springer, 2019, 113 (4), pp.3949-3965. ⟨10.1007/s13398-018-0596-7⟩. ⟨hal-02907173⟩

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