Cohomology of groups
Cohomology of groups
This chapter discusses the cohomology of groups. The cohomology of groups is one of the crossroads of mathematics. It has its origins in the representation theory, class field theory, and algebraic topology. The theory of cohomology of groups in degrees higher than two really begins with a theorem in algebraic topology. The links between algebraic topology and the group theory lead naturally to the idea of cohomological finiteness conditions. It is useful to compare this with the idea of a finiteness condition in the abstract group theory. The latter notion, prevalent in the work of Philip Hall and other influential groups theorists of some 30 years ago, has had a powerful influence on the study of abstract infinite groups. Furthermore, one advantage of cohomology over homology is the existence of cup products and Yoneda products. Yoneda products are defined in terms of composition of maps.
978-0444817792
917-950
Benson, D. J.
6b6a9c9b-b1b0-42ad-bcd2-c156c3d0ca2c
Kropholler, P. H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
August 1995
Benson, D. J.
6b6a9c9b-b1b0-42ad-bcd2-c156c3d0ca2c
Kropholler, P. H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Benson, D. J. and Kropholler, P. H.
(1995)
Cohomology of groups.
In,
James, I.M.
(ed.)
Handbook of Algebraic Topology.
Amsterdam, NL.
North-Holland,, .
(doi:10.1016/B978-044481779-2/50019-5).
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Abstract
This chapter discusses the cohomology of groups. The cohomology of groups is one of the crossroads of mathematics. It has its origins in the representation theory, class field theory, and algebraic topology. The theory of cohomology of groups in degrees higher than two really begins with a theorem in algebraic topology. The links between algebraic topology and the group theory lead naturally to the idea of cohomological finiteness conditions. It is useful to compare this with the idea of a finiteness condition in the abstract group theory. The latter notion, prevalent in the work of Philip Hall and other influential groups theorists of some 30 years ago, has had a powerful influence on the study of abstract infinite groups. Furthermore, one advantage of cohomology over homology is the existence of cup products and Yoneda products. Yoneda products are defined in terms of composition of maps.
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Published date: August 1995
Organisations:
Mathematical Sciences
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Local EPrints ID: 349605
URI: http://eprints.soton.ac.uk/id/eprint/349605
ISBN: 978-0444817792
PURE UUID: 844ee112-4bec-4b7e-9d90-3e0fbc5afe45
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Date deposited: 09 Apr 2013 15:55
Last modified: 15 Mar 2024 03:46
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Author:
D. J. Benson
Editor:
I.M. James
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