# Mayer–Vietoris sequences and equivariant $K$-theory rings of toric varieties

@article{Holm2019MayerVietorisSA,
title={Mayer–Vietoris sequences and equivariant \$K\$-theory rings of toric varieties},
author={Tara S. Holm and Gareth Williams},
journal={Homology, Homotopy and Applications},
year={2019}
}
• Published 31 January 2018
• Mathematics
• Homology, Homotopy and Applications
We apply a Mayer-Vietoris sequence argument to identify the Atiyah-Segal equivariant complex K-theory rings of certain toric varieties with rings of integral piecewise Laurent polynomials on the associated fans. We provide necessary and sufficient conditions for this identification to hold for toric varieties of complex dimension 2, including smooth and singular cases. We prove that it always holds for smooth toric varieties, regardless of whether or not the fan is polytopal or complete…
2 Citations

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