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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