Summer Lectures in Geometry 

11/06/2007, 14:00 — 15:00 — Room P3.10, Mathematics Building
Hansjörg Geiges, Mathematical Institute of the University of Cologne, Germany

Contact Manifolds — Classification results and applications to Geometric Topology (I)

Legendrian knots and the Whitney-Graustein Theorem

The first lecture will be a colloquium-style talk. I shall give a very gentle introduction to some basic concepts of contact geometry, notably concerning knots in contact 3-manifolds. This will be used to give a contact geometric proof of the Whitney-Graustein theorem in planar geometry: immersions of the circle in the 2-plane are classified, up to regular homotopy, by their rotation number.