Algebraic and Geometric Topology 2 (2002),
paper no. 26, pages 537-562.
Farrell cohomology of low genus pure mapping class groups with punctures
Qin Lu
Abstract.
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
AMS subject classification.
Primary: 55N35, 55N20.
Secondary: 57T99, 57R50.
DOI: 10.2140/agt.2002.2.537
E-print: arXiv:math.AT/0207174
Submitted: 3 October 2001.
(Revised: 29 April 2002.)
Accepted: 26 June 2002.
Published: 19 July 2002.
Notes on file formats
Qin Lu
Department of Mathematics, Lafayette College
Easton, PA 18042, USA
Email: luq@Lafayette.edu
AGT home page
