In:
Proceedings of the Edinburgh Mathematical Society, Cambridge University Press (CUP), Vol. 26, No. 2 ( 1983-06), p. 173-179
Abstract:
In a previous paper [ 1 ] we constructed a free resolution for a class of groups which include Fuchsian groups with compact orbit spaces [ 2, 3 ], infinite polyhedral groups, plane crystallographic groups p 2 , p 3 , p 4 and p 6 and Dyck's groups [ 4 ], and used this resolution for computation of the integral homology and cohomology of these groups. Lyndon [ 5 ] determined the cohomology of groups with a single defining relation. The plane crystallographic groups p 1 and pg and Artin's braid group B 3 are among these groups. In this paper we have constructed free resolutions for certain classes of groups–resolutions which are particularly suitable for direct computation of the homology and the cohomology of these groups for any coefficient module. These classes of groups include the plane crystallographic groups pm , cm and pgg . We have computed the integral homology and cohomology from each of the free resolutions obtained.
Type of Medium:
Online Resource
ISSN:
0013-0915
,
1464-3839
DOI:
10.1017/S0013091500016886
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1983
detail.hit.zdb_id:
1465484-2
SSG:
17,1
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