On Mapping Class Groups of Non-Orientable Surfaces

Explore the structure and cohomology of mapping class groups of non-orientable surfaces in this 54-minute lecture by Miguel Xicoténcatl from CINVESTAV. Delve into recent research findings, including the cohomology of mapping class groups with marked points for projective planes and Klein bottles, and their connection to characteristic classes of surface bundles. Examine the Nielsen realization theorem for non-orientable surfaces and the non-existence of a section for the natural projection from Diff(N_g) to Mod(N_g). Gain insights into the systematic study of Farrell cohomology of Mod(N_g; k) for g≥2, based on collaborative work with M. Maldonado, C. Hidber, N. Colin, and R. Jiménez.

Miguel Xicoténcatl, CINVESTAV: On mapping class groups of non-orientable surfaces