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Results tagged with group-cohomology
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user 17734
In mathematics, 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.
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Groups with trivial rational homology and their finite index subgroups
Thompson's group $T$ gives an example, i.e. if $T \le H$ has finite index, then $H^\ast(H;\mathbb{Q}) \neq 0$.
More specifically, there is always a non-trivial class in $H^4(H;\mathbb{Q})$.
Proof: …
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