Math 757 — Topics in Topology: Rational Homotopy Theory

Fall 2002

Instructor: James Conant

Time: TR 8:40-9:55

Room: Malott 206

It is difficult to calculate the higher homotopy groups of spheres. In fact, there is no sphere for which all of the higher homotopy groups is known. On the other hand, computing the rank of these groups is quite easy. For even dimensional spheres there is only one group with nonzero rank whereas for odd dimensional spheres there are two groups with nonzero rank. All other groups are torsion. This is a sample application of the main subject of this course, rational homotopy theory. The prerequisite for this course is a basic knowledge of algebraic topology.