On the Farrell cohomology of the mapping class group of non-orientable surfaces
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- by Graham Hope and Ulrike Tillmann PDF
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Abstract:
We study the unstable cohomology of the mapping class groups $\mathcal {N}_g$ of non-orientable surfaces of genus $g$. In particular, we determine for all genus $g$ and all primes $p$ when the group $\mathcal {N}_g$ is $p$-periodic.
To this purpose we show that $\mathcal {N}_g$ is a subgroup of the mapping class group $\Gamma _{g-1}$ of an orientable surface of genus $g-1$ and deduce that $\mathcal {N}_g$ has finite virtual cohomological dimension. Furthermore, we describe precisely which finite groups of odd order are subgroups of $\mathcal {N}_g$.
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Additional Information
- Graham Hope
- Affiliation: Mathematical Institute, Oxford University, Oxford OX1 3LB, United Kingdom
- Email: hope@maths.ox.ac.uk
- Ulrike Tillmann
- Affiliation: Mathematical Institute, Oxford University, Oxford OX1 3LB, United Kingdom
- Email: tillmann@maths.ox.ac.uk
- Received by editor(s): September 25, 2007
- Received by editor(s) in revised form: January 18, 2008
- Published electronically: September 3, 2008
- Communicated by: Paul Goerss
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 393-400
- MSC (2000): Primary 57M60; Secondary 20J05, 57S05
- DOI: https://doi.org/10.1090/S0002-9939-08-09507-5
- MathSciNet review: 2439465