On the Farrell Cohomology of the Mapping Class Group of Non-orientable Surfaces Graham Hope and Ulrike Tillmann
نویسنده
چکیده
Because of their close relation to moduli spaces of Riemann surfaces, the mapping class groups of orientable surfaces have been the attention of much mathematical research for a long time. Less well studied is the mapping class group of nonorientable surfaces. But recently, the study of mapping class groups has also been extended to the non-orientable case. This paper contributes to this programme. While Wahl [W] proved the analogue of Harer’s (co)homology stability to the nonoriented case, we concentrate here on the unstable part of the cohomology. In particular, we study the question of p-periodicity.
منابع مشابه
On the Farrell Cohomology of the Mapping Class Group of Non-orientable Surfaces
We study the unstable cohomology of the mapping class groups Ng of non-orientable surfaces of genus g. In particular, we determine for all genus g and all primes p when the group Ng is p-periodic. To this purpose we show that Ng is a subgroup of the mapping class group Γg−1 of an orientable surface of genus g − 1 and deduce that Ng has finite virtual cohomological dimension. Furthermore, we des...
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