MAGMA Computational Algebra System

Cohomology

Dual(G) : GrpAb -> GrpAb, Map

Computes the dual group G^ * of G and a map M from G x G^ * to Z/mZ for m the exponent of G that allows G^ * to act on G. G must be finite.

H2_G_QmodZ(G) : GrpAb -> GrpAb, Map

Computes H := H²(G, Q/Z) and a map f : H to (G x G to Z/mZ) that will give the cocycles as maps from G x G to Z/mZ. m := #G.

Res_H2_G_QmodZ(U, H2) : GrpAb, GrpAb -> GrpAb, Map

For a subgroup U of G and H2 = H²(G, Q/Z) computes H²(U, Q/Z) in a compatible way together with the restriction map into H2.

H2 must be the result of H2_G_QmodZ as this function relies on the attributes stored in there.