OAI/Geometry/HyperbolicGroups/BasedSquareContraction.lean

GitHub source file

14 declarations, 0 contain sorry, 0 declared as axioms

A vanishing actual pi-2 obstruction constructs a continuous square contraction with four independently prescribed edge contractions.

  1. def OAI.HyperbolicObstruction.BasedSquareContraction.facePath line 21
  2. def OAI.HyperbolicObstruction.BasedSquareContraction.faceObstruction line 26
  3. def OAI.HyperbolicObstruction.BasedSquareContraction.loopSquare line 31
  4. lemma OAI.HyperbolicObstruction.BasedSquareContraction.loopSquare_bottom line 35
  5. lemma OAI.HyperbolicObstruction.BasedSquareContraction.loopSquare_top line 38
  6. lemma OAI.HyperbolicObstruction.BasedSquareContraction.loopSquare_left line 41
  7. lemma OAI.HyperbolicObstruction.BasedSquareContraction.loopSquare_right line 44
  8. def OAI.HyperbolicObstruction.BasedSquareContraction.contraction line 49

    Source documentation

    Literal face homotopy. Its domain is the actual closed square prism.

    def contraction : C(I × (I × I),X) :=
…
  9. lemma OAI.HyperbolicObstruction.BasedSquareContraction.contraction_initial line 52
  10. lemma OAI.HyperbolicObstruction.BasedSquareContraction.contraction_final line 58
  11. lemma OAI.HyperbolicObstruction.BasedSquareContraction.contraction_bottom line 64
  12. lemma OAI.HyperbolicObstruction.BasedSquareContraction.contraction_right line 69
  13. lemma OAI.HyperbolicObstruction.BasedSquareContraction.contraction_left line 74
  14. lemma OAI.HyperbolicObstruction.BasedSquareContraction.contraction_top line 79