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Group cohomology
Tools for studying groups based on techniques from algebraic topology
Group cohomology
In mathematics (more specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group. By treating the G-module as a kind of topological space with elements of G n {\displaystyle G^{n}} representing n-simplices, topological properties of the space may be computed, such as the set of cohomology groups H n ( G , M ) {\displaystyle H^{n}(G,M)} . The cohomology groups in turn provide insight into the structure of the group G and G-module M themselves. Group cohomology plays a role in the investigation...
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