euler(KClass) -- computes the equivariant Euler characteristic of an equivariant K-class

Synopsis

Function: euler
Usage:

euler C
Inputs:
- C, an equivariant K-class,
Outputs:
- a ring element, in the character ring of the torus of the GKM variety on which C is defined

Description

This method computes the pushforward of a KClass on a GKMVariety $X$ along the structure map $X \to pt$, where $pt$ is a point with trivial torus-action.

i1 : PP3 = projectiveSpace 3

o1 = a "GKM variety" with an action of a 4-dimensional torus

o1 : GKMVariety

i2 : O1 = ampleKClass PP3

o2 = an "equivariant K-class" on a GKM variety 

o2 : KClass

i3 : euler O1

o3 = T  + T  + T  + T
      0    1    2    3

o3 : ZZ[T ..T ]
         0   3

Ways to use this method: