1 / 32

GEOMETRIC TOPOLOGY

GEOMETRIC TOPOLOGY. MAIN GOAL: TO PROVE TOPOLOGICAL RESULTS ABOUT SMOOTH MANIFOLDS BY ENDOWING THEM WITH ADDITIONAL GEOMETRIC STRUCTURES Example of a geometric structure: Riemannian metric. GEOMETRIC TOPOLOGY OF LOW DIMENSIONAL MANIFOLDS. SYMPLECTIC FOUR DIMENSIONAL MANIFOLDS

aadi
Download Presentation

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 Example of a geometric structure: Riemannian metric

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

  3. CONTACT 3-MANIFOLDS

  4. Tight versus overtwisted

  5. Local structure

  6. Global structure

  7. Open books

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

  9. Abstract open books

  10. Mapping torus

  11. Stabilization of an open book

  12. Stabilization of an open book

  13. Open books and contact structures

More Related