2. Example of a geometric structure: Riemannian metric
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

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

8. CONTACT 3-MANIFOLDS

15. Tight versus overtwisted

17. Local structure

18. Global structure

22. Open books

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

24. Abstract open books

25. Mapping torus

27. Stabilization of an open book

28. Stabilization of an open book

29. Open books and contact structures