On the Farrell cohomology of the mapping class group of non-orientable surfaces

Journal article

We study the unstable cohomology of the mapping class groups N g of non-orientable surfaces of genus g. In particular, we determine for all genus g and all primes p when the group N g is p-periodic. To this purpose we show that N g is a subgroup of the mapping class group Γ g-1 of an orientable surface of genus g - 1 and deduce that N g has finite virtual cohomological dimension. Furthermore, we describe precisely which finite groups of odd order are subgroups of N g. © 2008 American Mathematical Society.

Authors: Hope, G; Tillmann, U

• Publication status: Published
• Journal: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
• Volume: 137
• Issue: 1
• Pages: 393-400
• Publication date: 2009-01-01
• DOI: 10.1090/S0002-9939-08-09507-5
• ISSN: 0002-9939
• Language: English