Group homology is the homology dual of group cohomology.

See for instance at *group cohomology – In terms of homological algebra* and replace Ext by Tor.

Accordingly, the group homology of a discrete group $G$ is equivalently the ordinary homology of its classifying space $B G$ (the Eilenberg-MacLane space $K(G,1)$):

$H^{grp}_\bullet(G)
\;\simeq\;
H_\bullet\big( B G \big)
\,.$

(eg. Brown 1982, §4.1).

- Kenneth Brown,
*The Homology of a Group*, Chapter II of:*Cohomology of Groups*, Graduate Texts in Mathematics,**87**, Springer (1982) [doi:10.1007/978-1-4684-9327-6]

Last revised on November 26, 2023 at 15:16:58. See the history of this page for a list of all contributions to it.