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