Poincaré-Reeb Graphs of Real Algebraic Domains

Poincaré-Reeb Graphs of Real Algebraic Domains

Centre International de Rencontres Mathématiques via YouTube Direct link

Intro

1 of 32

1 of 32

Intro

Class Central Classrooms beta

YouTube videos curated by Class Central.

Classroom Contents

Poincaré-Reeb Graphs of Real Algebraic Domains

Automatically move to the next video in the Classroom when playback concludes

  1. 1 Intro
  2. 2 Setting and goals
  3. 3 Algebraic domains
  4. 4 Overview
  5. 5 The Poincaré-Reeb graph
  6. 6 The asymptotic Poincaré-Reeb tree
  7. 7 Reformulation
  8. 8 The polar curve
  9. 9 Choosing a generic projection
  10. 10 The generic asymptotic Poincaré-Reeb tree
  11. 11 The discriminant locus
  12. 12 Genericity hypotheses
  13. 13 1. Positive asymptotic snake
  14. 14 2. Arnold's snake (one variable)
  15. 15 Idea of the proof
  16. 16 The construction
  17. 17 Separable permutations
  18. 18 Nonseparable permutation - example
  19. 19 Separable tree
  20. 20 Passing to the univariate case
  21. 21 The contact tree
  22. 22 Answer in the univariate case
  23. 23 Construction of the desired bivariate polynomial f
  24. 24 Flip-Flop Algorithm
  25. 25 Vertical planes
  26. 26 The topological critical set
  27. 27 Domain of finite type
  28. 28 Vertical equivalence
  29. 29 Complete invariant
  30. 30 Invariance of the Euler characteristic
  31. 31 Strategy of the proof
  32. 32 Non-compact Poincaré-Reeb graphs

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.