Equivariant $K$-theory of even-dimensional complex quadrics

Abstract

The aim of this paper is to describe the torus equivariant $K$-ring of even-dimensional complex quadrics by studying the graph equivariant $K$-theory of their corresponding GKM graphs. This involves providing a presentation for its graph equivariant $K$- ring in terms of generators and relations. This parallels the description of the equivariant cohomology ring of even-dimensional complex quadrics due to Kuroki.

18 pages

References in corpus (6)

• Lusztig's conjecture as a moment graph problem
• The cohomology ring of the GKM graph of a flag manifold of classical type
• An Orlik-Raymond type classification of simply connected six-dimensional torus manifolds with vanishing odd degree cohomology
• Upper bounds for the dimension of tori acting on GKM manifolds
• Graph equivariant cohomological rigidity for GKM graphs
• Equivariant $K$-theory of GKM bundles