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GKMVarieties :: KClass

KClass -- the class of all equivariant K-classes


For $X$ a GKM variety with an action of a torus $T$ whose character ring is $R$, a $T$-equivariant $K$-class $C \in K_T^0(X)$ of is encoded by its image in $K_T^0(X^T) = \prod_{x\in X^T} R$, under the injective restriction map $K_T^0(X) \to K_T^0(X^T)$. See [Corollary 5.12; VV03] or [Corollary A.5; RK03] for details.

A KClass C is a HashTable consisting of two keys:

  • variety, whose value is a GKMVariety of which C is a K-class of
  • KPolynomials, whose value is a HashTable; its keys are X.points and the values are Laurent polynomials in the character ring representing the values of the K-class under the restriction map.

See also

Functions and methods returning an equivariant K-class :

Methods that use an equivariant K-class :

For the programmer

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