Equivariant $K$-theory of quasitoric manifolds

Abstract

Let $X(Q,\Lambda)$ be a quasitoric manifold associated to a simple convex polytope $Q$ and characteristic function $\Lambda$. Let $T\cong (\mathbb{S}^1)^n$ denote the compact $n$-torus acting on $X=X(Q,\Lambda)$. The main aim of this article is to give a presentation of the $T$-equivariant $K$-ring of $X$, as a Stanley-Reisner ring over $K^*(pt)$. We also derive the presentation for the ordinary $K$-ring of $X$.