Farrell cohomology of low genus pure mapping class groups with punctures

In this paper, we calculate the $p$ –torsion of the Farrell cohomology for low genus pure mapping class groups with punctures, where $p$ is an odd prime. Here, ‘low genus’ means $g = 1, 2, 3$ ; and ‘pure mapping class groups with punctures’ means the mapping class groups with any number of punctures, where the punctures are not allowed to be permuted. These calculations use our previous results about the periodicity of pure mapping class groups with punctures, as well as other cohomological tools. The low genus cases are interesting because we know that the high genus cases can be reduced to the low genus ones. Also, the cohomological properties of the mapping class groups without punctures are closely related to our cases.

Keywords

Farrell cohomology, pure mapping class group with punctures, fixed point data, periodicity

Mathematical Subject Classification 2000

Primary: 55N35, 55N20

Secondary: 57T99, 57R50

References

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Publication

Received: 3 October 2001

Revised: 29 April 2002

Accepted: 26 June 2002

Published: 19 July 2002

Authors

Qin Lu
Department of Mathematics Lafayette College Easton, PA 18042 USA

Volume 2, issue 1 (2002)

Qin Lu