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 \(H^i(G, \ldots)\).

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

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

NewCodomain: Any                          Default: false
Level      : RngIntElt                    Default: false

Given a cochain \(c: G^i \to X\) and a (transversal) map \(H \to G\), return the inflation (lift) of \(c\) to \(H\), ie. a cochain \(d:H^i \to X\) 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.