# Questions tagged [group-homology]

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### Group homology $\mathrm{SL}_2$ acting on $\mathrm{Sym}^g$

Let $k$ be a field. We write $\mathrm{Sym}^g(k^2)$ for the $g$-th symmetric power of the (a?) standard representation of $\mathrm{GL}_2(k)$ ($g\geq 0$ an integer). Here I consider $\mathrm{Sym}^g(k^2)$...
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Let $Sp(2n,{\mathbb R})$ be the symplectic group and $H_3(Sp(2n,{\mathbb R});{\mathbb Z})$ its 3rd group homology (i.e., for the group with the discrete topology). It is known that $$H_3(Sp(2n,{\... 1answer 241 views ### Homology of solvable Lie groups made discrete In what follows "homology" will mean group homology, i.e. H_*(BG^\delta;{\mathbf R}) for the group G with the discrete topology. It is well-known how to compute the homology of abelian groups, ... 0answers 166 views ### Is the Tensor/Exterior square G\otimes G or G\wedge G of infinite p-group also a p-group? Let G be an infinite countable p-group. Is it true that G\otimes G or G\wedge G are also p-groups? (where G acts on itself by conjugation). For simplicity, you can consider that G=[G,G], and ... 0answers 80 views ### Methods for showing homology of a subgroup survives to the larger group Suppose we have an inclusion of groups G_1<G_2. I am curious about what methods there are out there for analyzing the map H_k(G_1;\mathbb Q)\to H_k(G_2;\mathbb Q). In particular, what are tools ... 1answer 338 views ### Cup-products and Transgression maps. This question is related to Lyndon-Hochschild-Serre spectral sequence and cup products. I have the followin result by J.S Milne in his book Arithmetic duality theorems pg 105. Let$$0 \rightarrow C \...
I am interested in whether the transgression maps for group cohomology and group homology are related via a version of the universal coefficient theorem. Let $G$ be a group, $H$ a normal subgroup of \$...