Mapping Class Groups of Non-orientable Surfaces and Their Cohomology

Explore a 39-minute lecture on mapping class groups of non-orientable surfaces, where the structure and cohomology of mapping class groups Mod(N_g) of non-orientable surfaces N_g are examined in detail. Learn about the cohomology of mapping class groups with marked points of the projective plane and Klein bottle, and understand their connection to characteristic classes of surface bundles. Discover the Nielsen realization theorem for non-orientable surfaces and examine the non-existence of a section for the natural projection from Diff(N_g) to Mod(N_g). Delve into a systematic study of the Farrell cohomology of Mod(N_g; k) for g2, featuring collaborative research work with M. Maldonado, C. Hidber, N. Colin, and R. Jiménez.