Mathematics 104, Winter 2009
Professor: Vladimir Chernov
Course Description and Material: This course introduces the basic concepts of knot theory, theory of manifolds and contact topology. Topics include invariants of finite order, linking number, Gauss diagrams, braids, Heegard splitting, automorphisms of surfaces, surgery, branched covers, contact manifolds and Legendrian knots. We will discuss applications to classification of 3-manifolds and to Lorentz space-times. The course assumes the knowledge of point set topology, and of abstract algebra. It is better if the students have basic knowledge of differential geometry and of the coverings and the fundamental group, but these topics will be refreshed.