OAI/GroupTheory/PolycyclicRecognition/Algebra/DixmierRegularityFromTopology.lean

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Smooth regularity from the topological Dixmier chart

Given a global exponential homeomorphism, the faithful triangular representation and the injective differential of its exponential prove smoothness of the chart and its inverse, as needed for metric comparison.

  1. theorem OAI.PolycyclicRecognition.dixmier_exponential_smooth_chart line 27
  2. theorem OAI.PolycyclicRecognition.dixmierExponentialDiffeomorphismInput_of_topological line 94

    Source documentation

    The smooth regularity needed by the metric application is derived; only a global topological exponential chart is a hypothesis.

    theorem dixmierExponentialDiffeomorphismInput_of_topological
        (dixmier : DixmierExponentialInput (E := E) (G := G)) :
    …

    Mentions: OAI.PolycyclicRecognition.DixmierExponentialInput