Download
slide1 n.
Skip this Video
Loading SlideShow in 5 Seconds..
GEOMETRIC TOPOLOGY PowerPoint Presentation
Download Presentation
GEOMETRIC TOPOLOGY

GEOMETRIC TOPOLOGY

460 Views Download Presentation
Download Presentation

GEOMETRIC TOPOLOGY

- - - - - - - - - - - - - - - - - - - - - - - - - - - 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