On the Nielsen Realization Problem and Cohomology of Mapping Class Groups of Non-orientable Surfaces

This course covers the Nielsen realization problem and the cohomology of mapping class groups of non-orientable surfaces. By the end of the course, students will be able to understand the Nielsen realization problem for non-orientable surfaces with marked points, classify normalizers of cyclic subgroups, and study the p-periodicity of the group. The course teaches skills such as analyzing fixed point data for diffeomorphisms, classifying normalizers of prime order cyclic subgroups, and determining the p-primary component of Farrell cohomology in certain cases. The teaching method involves theoretical explanations, proofs, and applications of the concepts discussed. This course is intended for individuals interested in advanced topics in mathematics, particularly in the fields of topology, geometry, and group theory.