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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

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GEOMETRIC TOPOLOGY

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  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

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