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2002 Farrell cohomology of low genus pure mapping class groups with punctures
Qin Lu
Algebr. Geom. Topol. 2(1): 537-562 (2002). DOI: 10.2140/agt.2002.2.537


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.


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Qin Lu. "Farrell cohomology of low genus pure mapping class groups with punctures." Algebr. Geom. Topol. 2 (1) 537 - 562, 2002.


Received: 3 October 2001; Revised: 29 April 2002; Accepted: 26 June 2002; Published: 2002
First available in Project Euclid: 21 December 2017

zbMATH: 1025.57023
MathSciNet: MR1917066
Digital Object Identifier: 10.2140/agt.2002.2.537

Primary: 55N20, 55N35
Secondary: 57R50, 57T99

Rights: Copyright © 2002 Mathematical Sciences Publishers


Vol.2 • No. 1 • 2002
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