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arXiv · 2401.17240

Isomorphisms in K-theory from isomorphisms in groupoid homology theories

Alistair Miller
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Abstract

We prove that for torsion-free amenable ample groupoids, an isomorphism in groupoid homology induced by an \'etale correspondence yields an isomorphism in the K-theory of the associated $\mathrm{C}^\ast$-algebras. We apply this to extend X. Li's K-theory formula for left regular inverse semigroup $\mathrm{C}^\ast$-algebras. These results are obtained by developing the functoriality of the ABC spectral sequence.

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Alistair Miller. 2024-01-30. Isomorphisms in K-theory from isomorphisms in groupoid homology theories. https://arxiv.org/abs/2401.17240

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