Workshop on "Algebra and Geometry of Configuration Spaces and related structures" June 21th through 25th

On mapping class groups of non-orientable surfaces

speaker: Miguel Xicotencatl (Centro de Investigacion y de Estudios Avanzados)

abstract:

The mapping class group (m.c.g.) Γ_g⁺ of an oriented surface M_g, is the group of isotopy classes of orientation preserving diffeomorphisms of M_g. Variations of this group include the full m.c.g. Γ_g^±, and the m.c.g. with marked points. Recently, the study of m.c.g.’s has also been extended to the non-orientable case. When considering all diffeomorphims, one shows the m.c.g. of a surface M (oriented or not) with k marked points, surjects onto the full m.c.g. Γ(M) with kernel Γ^k(M). Moreover, using configuration spaces we construct a space with fundamental group Γ^k(M). In the case when M is the projective plane or the Klein bottle, we use these spaces to study the cohomology of Γ^k(M) and groups related to the braid groups of M. This is joint work with Miguel A. Maldonado.

timetable:
Thu 24 Jun, 17:30 - 18:00, Aula Dini
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