The University of Southampton
University of Southampton Institutional Repository

Cohomology of groups

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
North-Holland,
Benson, D. J.
6b6a9c9b-b1b0-42ad-bcd2-c156c3d0ca2c
Kropholler, P. H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
James, I.M.
Benson, D. J.
6b6a9c9b-b1b0-42ad-bcd2-c156c3d0ca2c
Kropholler, P. H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
James, I.M.

Benson, D. J. and Kropholler, P. H. (1995) Cohomology of groups. In, James, I.M. (ed.) Handbook of Algebraic Topology. Amsterdam, NL. North-Holland,, pp. 917-950. (doi:10.1016/B978-044481779-2/50019-5).

Record type: Book Section

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.

Full text not available from this repository.

More information

Published date: August 1995
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 349605
URI: https://eprints.soton.ac.uk/id/eprint/349605
ISBN: 978-0444817792
PURE UUID: 844ee112-4bec-4b7e-9d90-3e0fbc5afe45

Catalogue record

Date deposited: 09 Apr 2013 15:55
Last modified: 18 Oct 2018 16:32

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×