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 describe precisely which finite groups of odd order are subgroups of Ng .


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