MAGMA Computational Algebra System

Other operations on cohomology modules

CorestrictionMapImage(G, C, c, i):Grp, ModCoho, UserProgram, RngIntElt -> UserProgram

CorestrictCocycle(G, C, c, i): Grp, ModCoho, UserProgram, RngIntElt -> UserProgram

Given an i-cochain c for the cohomology module C which has to be defined wrt. to some subgroup U of G, return the corestriction of c to Hⁱ(G, ... ).

InflationMapImage(M, c) : Map, UserProgram -> UserProgram

LiftCocycle(M, c): Map, UserProgram -> UserProgram

    NewCodomain: Any                    Default: false

    Level: RngIntElt                    Default: false

Given a cochain c: Gⁱ to X and a (transversal) map H to G, return the inflation (lift) of c to H, ie. a cochain d:Hⁱ to X defined by d(h) := c(M(h)). If Level is given c is assumed to be in the cohomology group of that level, ie. i := Level. If Level is not specified, Magma tries its best to guess the correct level.

If NewCodomain is given, the values of d are coerced into this structure.

CoboundaryMapImage(M, i, c) : ModCoho, RngIntElt, UserProgram -> UserProgram

For a cohomology module M, a level i and a i-cochain c (as a user program), return a i + 1-coboundary as obtained from the cohomological coboundary operator.