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

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, 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 𝒜(1)–modules.

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KO–theory, toric manifolds, quasitoric manifolds
Mathematical Subject Classification 2010
Primary: 14M25, 19E20, 55N15
Secondary: 57N65
Received: 10 April 2019
Revised: 13 June 2019
Accepted: 27 July 2019
Published: 4 November 2020
Li Cai
Department of Mathematical Sciences
Xi’an Jiaotong-Liverpool University
Suyoung Choi
Department of Mathematics
Ajou University
South Korea
Hanchul Park
Department of Mathematics Education
Jeju National University
South Korea