OAI/Geometry/SurfaceImmersion/Whitney/CrosscapFrameHomotopy.lean

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5 declarations, 0 contain sorry, 0 declared as axioms

A concrete formal homotopy reduces the derivative of one standard crosscap to its planar normal-defect frame. The homotopy is injective away from the original singular point at every parameter.

  1. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapFrameHomotopy line 14
  2. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapFrameHomotopy_smooth line 18
  3. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapFrameHomotopy_one line 38
  4. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapFrameHomotopy_zero line 47
  5. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapFrameHomotopy_injective_iff line 54