Algebraic Topology II

The goal with the course is to give a solid background for studies in topology, and develop geometrical ideas and algebraic methods introduced in Algebraic Topology I. The course supports studies in related subjects as algebra, geometry and theoretical physics. Subjects to be treated are singular (co)homology theory: Poincaré duality and Steenrod operations. Complex K-theory, (co)bordism theory, generalized cohomology theories and spectra. Formal group laws and genera.

1. Knowledge. The student has knowledge of advanced topics in algebraic topology, such as Poincaré duality, Steenrod operations and generalized homology and cohomology theories, in particular K-theory and bordism theories.

2. Skills. The student is able to apply his or her knowledge of algebraic topology to formulate and solve problems of a geometric-topological nature in mathematics and theoretical physics.

Lectures and exercises.