The Equivariant Grothendieck Groups of the Russell-Koras Threefolds

http://dx.doi.org/10.4153/CJM-2001-001-x
Canad. J. Math. 53(2001), 3-32

  Published:2001-02-01
 Printed: Feb 2001

The Russell-Koras contractible threefolds are the smooth affine threefolds having a hyperbolic $\mathbb{C}^*$-action with quotient isomorphic to the corresponding quotient of the linear action on the tangent space at the unique fixed point. Koras and Russell gave a concrete description of all such threefolds and determined many interesting properties they possess. We use this description and these properties to compute the equivariant Grothendieck groups of these threefolds. In addition, we give certain equivariant invariants of these rings.