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arXiv · 2509.24145

Spectral continuity for \'etale groupoids with the Rapid decay property

Tom Stoiber
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Abstract

We show that the reduced groupoid C*-algebras of continuous fields of \'etale groupoids satisfying the rapid decay property yield continuous fields of C*-algebras. This establishes a new sufficient criterion that applies in the non-amenable case where the full and reduced groupoid algebras may differ. Potential applications include convergence of spectra in inverse systems of finite-index subgroups and magnetic models on hyperbolic lattices.

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Tom Stoiber. 2025-09-29. Spectral continuity for \'etale groupoids with the Rapid decay property. https://arxiv.org/abs/2509.24145

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