$K$-theory of $\mbox{hyperK\"ahler}$ toric manifolds

TL;DR

This paper provides a presentation of the topological K-ring of toric hyperK"ahler manifolds, analogous to their cohomology ring, enhancing understanding of their topological structure.

Contribution

It offers a novel description of the topological K-ring for toric hyperK"ahler manifolds using generators and relations.

Findings

Explicit presentation of K^*(X) in terms of generators and relations

Analogous description to the cohomology ring of these manifolds

Advances the understanding of topological invariants of hyperK"ahler toric manifolds

Abstract

Let $X$ be a toric $\mbox{hyperK\"ahler}$ manifold. The purpose of this note is to describe the topological $K$-ring $K^*(X)$ of $X$. We give a presentation for the topological $K$-ring in terms of generators and relations similar to the known description of the cohomology ring of these manifolds.