1 / 53

GEOMETRIC TOPOLOGY

GEOMETRIC TOPOLOGY. MAIN GOAL: TO PROVE TOPOLOGICAL RESULTS ABOUT SMOOTH MANIFOLDS BY ENDOWING THEM WITH ADDITIONAL GEOMETRIC STRUCTURES. GEOMETRIC TOPOLOGY OF LOW DIMENSIONAL MANIFOLDS. SYMPLECTIC FOUR DIMENSIONAL MANIFOLDS CONTACT THREE DIMENSIONAL MANIFOLDS. Property P.

haru
Télécharger la présentation

GEOMETRIC TOPOLOGY

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. GEOMETRIC TOPOLOGY MAIN GOAL: TO PROVE TOPOLOGICAL RESULTS ABOUT SMOOTH MANIFOLDS BY ENDOWING THEM WITH ADDITIONAL GEOMETRIC STRUCTURES

  2. GEOMETRIC TOPOLOGY OF LOW DIMENSIONAL MANIFOLDS SYMPLECTIC FOUR DIMENSIONAL MANIFOLDS CONTACT THREE DIMENSIONAL MANIFOLDS

  3. Property P

  4. CONTACT THREE DIMENSIONAL MANIFOLDS

  5. Frobenius Theorem

  6. Contact forms

  7. Contact structure

  8. Legendrian curve A curve in a contact 3-manifold is called Legendrian if it is everywhere tangent to the contact planes.

  9. Overtwisted Disk

  10. Tight versus overtwisted

  11. Tight versus overtwisted

  12. Darboux’s Theorem

  13. Contact Topology

  14. Global structure

  15. Global structure

  16. Classification of overtwisted contact structures Martinet+Lutz+Eliashberg Overtwisted contact structures are classified: There is, up to isotopy, a unique overtwisted contact structure in every homotopy class of oriented plane fields.

  17. Classification of tight contact structures?

  18. Convex surfaces

  19. 2002 Giroux’s ICM talk in Beijing

  20. Open books

  21. Complement of the Hopf link in the 3-sphere fibers over the circle

  22. Abstract open books

  23. Mapping torus M

  24. Stabilization of an open book

  25. Stabilization of an open book

  26. Open books and contact structures

  27. Etnyre’s Lemma

More Related