31 окт. 2018 г. · We are basically spelling out that group (co)homology is a functor in both variables. For conjugation by g∈G, we have two maps cg:H→gHg−1 ...

2 апр. 2021 г. · It is well-known that the singular homology of the classifying space of a group G is isomorphic to the group homology of G with coefficients in ...

18 апр. 2012 г. · When G acts trivially on M, the first homology group is just the abelianisation of G tensored with M, i.e. H1(G;M)=(G/[G,G])⊗ZM.

7 февр. 2020 г. · Let G be a group and H its subgroup (H need not to be normal). Consider a chain complex (C∗(G),∂) where Cn(G) is the free abelian group ...

4 февр. 2020 г. · Let G be a topological group. It has a classifying space BG, which has homology groups H∗BG. Changing the topology of G affects the space BG and ...

8 нояб. 2023 г. · We work with the first homology group H1(G,M). For any cyclic subgroup C⊆G, we consider the inclusion map iC:C↪G and the induced homomorphism ...

8 апр. 2018 г. · The question concerns the group homology or group cohomology of symmetric groups. The entries in groupprops.subwiki.org and in this MO post show the results.

2 июн. 2021 г. · If E is contractible with a free G action and E→E/G is a fibration, then the homotopy type of E/G only depends on G.

21 мар. 2021 г. · Regarding 2, one nice feature of group cohomology is that it converts a nonabelian structure into a (graded) commutative one. As a result, you ...

21 янв. 2010 г. · Essential theorems in group (co)homology · Hopf's formula - If G has presentation F/R, then H2(G)=R∩[F,F]/[F,R] · If G has torsion then Hn(G) ...