CONTACT STRUCTURES

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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

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GEOMETRIC TOPOLOGY OF LOW DIMENSIONAL MANIFOLDS

• SYMPLECTIC FOUR DIMENSIONAL MANIFOLDS
• CONTACT THREE DIMENSIONAL MANIFOLDS

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CONTACT 3-MANIFOLDS
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Tight versus overtwisted
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Local structure
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Global structure
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Open books
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• Complement of the Hopf link in the 3-sphere
  fibers over the circle

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Abstract open books
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Mapping torus
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Stabilization of an open book
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• Stabilization of an open book

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Open books and contact structures
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