Mathematics 104, Winter 2009
General
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Topics
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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.