Middle East Technical University Department of Mathematics Fall 1995

SELECTED TOPICS IN LOW-DIMENSIONAL TOPOLOGY

An Informal Course/Seminar – Program

(1) Real and complex plane algebraic curves;

(2) Knots, links and braids;

(3) Elements of singularities theory;

(4) Around Poincare conjecture, exotic spheres;

(5) From Jordan theorem to Schönflies Conjecture (the horned sphere of Alexander etc.);

(6) Handle decomposition of manifolds, elements of Morse theory and cobordisms;

(7) Basic knowledge about 3-dimensional manifolds; surgery in the 3-sphere (Kirby calculus);

(8) Action of groups on manifolds; classical Lie groups; principal bundles;

(9) Introduction to 4-dimensional topology, intersection forms and exotic phenomena.