#### Volume 20, issue 5 (2020)

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On the $KO$–groups of toric manifolds

### Li Cai, Suyoung Choi and Hanchul Park

Algebraic & Geometric Topology 20 (2020) 2589–2607
##### Abstract

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 ${M}_{ℝ}$, the fixed points under the canonical conjugation on $M$. Following the work of Bahri and Bendersky (2000), 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 their mod $2$ cohomology groups as $\mathsc{𝒜}\left(1\right)$–modules.

##### Keywords
KO–theory, toric manifolds, quasitoric manifolds
##### Mathematical Subject Classification 2010
Primary: 14M25, 19E20, 55N15
Secondary: 57N65