nLab group homology




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 GG is equivalently the ordinary homology of its classifying space BGB G (the Eilenberg-MacLane space K(G,1)K(G,1)):

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

(eg. Brown 1982, §4.1).


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