Analytic Stratification in the Pfaffian Closure of an O-minimal Structure

  title={Analytic Stratification in the Pfaffian Closure of an O-minimal Structure},
  author={Jean-Marie Lion and Patrick Speissegger},
Introduction. Let U ⊆ R be open andω = a1dx1+·· ·+andxn a nonsingular, integrable 1-form onU of classC1, and let be the foliation onU associated toω. A leafL ⊆ U of is aRolle leaf if anyC1 curveγ : [0,1] → U with γ (0),γ (1) ∈ L is tangent to at some point, that is, ω(γ (t))(γ ′(t)) = 0 for somet ∈ [0,1]. Note that while a leaf of is in general only an immersed manifold, any Rolle leaf of is an embedded and closed submanifold of U . Throughout this paper, we fix an arbitrary o-minimal… CONTINUE READING

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