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

Authors:
Graham Hope and Ulrike Tillmann

Journal:
Proc. Amer. Math. Soc. **137** (2009), 393-400

MSC (2000):
Primary 57M60; Secondary 20J05, 57S05

Published electronically:
September 3, 2008

MathSciNet review:
2439465

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the unstable cohomology of the mapping class groups of non-orientable surfaces of genus . In particular, we determine for all genus and all primes when the group is -periodic.

To this purpose we show that is a subgroup of the mapping class group of an orientable surface of genus and deduce that has finite virtual cohomological dimension. Furthermore, we describe precisely which finite groups of odd order are subgroups of .

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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

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09507-5

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

Article copyright:
© Copyright 2008
American Mathematical Society