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
GEOMETRIC TOPOLOGY OF LOW DIMENSIONAL MANIFOLDS SYMPLECTIC FOUR DIMENSIONAL MANIFOLDS CONTACT THREE DIMENSIONAL MANIFOLDS
CONTACT 3-MANIFOLDS
Tight versus overtwisted
Local structure
Global structure
Open books
Complement of the Hopf link in the 3-sphere fibers over the circle
Abstract open books
Mapping torus
Stabilization of an open book
Stabilization of an open book
Open books and contact structures