On Mapping Class Groups of Non-Orientable Surfaces
Delve into an advanced mathematics lecture exploring mapping class groups of non-orientable surfaces. Learn about the Nielsen realization problem and its application to both orientable and non-orientable surfaces. Discover how finite subgroups of the mapping class group Mod(Ng, k) can be lifted to a subgroup of Diff(Ng, k) for non-orientable surfaces with marked points. Explore the contrast with orientable surfaces and understand why the natural projection from Diff(Ng) to Mod(Ng) does not admit a section for large g. Examine the p-periodicity of Mod(Ng, k) and the classification of normalizers of cyclic subgroups of prime order p. Gain insights into the determination of the p-primary component of the Farrell cohomology of Mod(Ng, k) in specific cases. This 55-minute talk, part of the "Geometry, Topology, Group Actions, and Singularities in the Americas" conference, offers a deep dive into cutting-edge research in algebraic topology, geometry, and mathematical physics.