OAI/Geometry/SurfaceImmersion/Whitney/CrosscapLinearCoordinates.lean

GitHub source file

8 declarations, 0 contain sorry, 0 declared as axioms

Explicit invertible linear coordinates adapted to the kernel of a crosscap.

  1. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapSourceLinear line 11
  2. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapSourceLinear_apply line 15
  3. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapSourceLinear_coordinates line 18
  4. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapSourceLinear_bijective line 24
  5. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapSourceEquiv line 43
  6. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapParameterLinear line 49

    Source documentation

    Reorder the linearized direction variables into the standard crosscap target coordinates.

    def crosscapParameterLinear (b : Bool) (t : ℝ) :
    (Base × ℝ) →L[ℝ] (Base × ℝ) :=
…
  7. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapParameterLinear_apply line 57
  8. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapParameterLinear_bijective line 65