# On the KO-groups of toric manifolds

## TL;DR

This paper provides an explicit formula for the real topological K-groups (KO-groups) of toric manifolds, linking their topology to fixed point sets and classifying extreme cases based on A(1) modules.

## Contribution

It introduces a formula for KO-groups of toric manifolds and characterizes extreme classes using A(1) modules, extending previous work on their topology.

## Key findings

- Explicit KO-group formula for toric manifolds
- Classification of manifolds via A(1) modules
- Connection between KO-groups and fixed point topology

## Abstract

In this paper we consider the real topological K-groups of a toric manifold M, which turns out to be closely related to the topology of the small cover MR, the fixed points under the canonical conjugation on M . Following the work of Bahri and Bendersky [2], we give an explicit formula for the KO-groups of toric manifolds, and then we characterize the two extreme classes of toric manifolds according to the two A(1) modules shown in [2].