EquivariantMap -- the class of all equivariant morphisms between GKM varieties

Description

Given two GKM varieties $X$ and $Y$, an equivariant morphism from $X$ to $Y$ induces a map from the torus-fixed points of $X$ to the torus-fixed points of $Y$.

A EquivariantMap C is a HashTable consisting of three keys:

source, whose value is a GKMVariety corresponding to the domain of f
target, whose value is a GKMVariety corresponding to the codomain of f
ptsMap, whose value is a HashTable; its keys are X.points and the values are points of Y.points that the key maps to.

Functions and methods returning an equivariant map :

compose(EquivariantMap,EquivariantMap) -- computes the composition of two equivariant morphisms
diagonalMap(GKMVariety) -- see diagonalMap -- constructs the diagonal morphism
EquivariantMap ** EquivariantMap -- computes the product of two equivariant morphisms
flagMap(GKMVariety,GKMVariety) -- see flagMap -- creates equivariant maps between generalized flag varieties
map(GKMVariety,GKMVariety,List) -- creates a EquivariantMap

Methods that use an equivariant map :

pullback(EquivariantMap) -- computes the pullback map of equivariant K-classes of an equivariant map
pushforward(EquivariantMap) -- see pushforward -- computes the pushforward map of equivariant K-classes of an equivariant map

For the programmer

The object EquivariantMap is a type, with ancestor classes HashTable < Thing.

EquivariantMap -- the class of all equivariant morphisms between GKM varieties

Description

See also

Functions and methods returning an equivariant map :

Methods that use an equivariant map :

For the programmer