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arXiv · 2108.00642

Strongly Quasi-local algebras and their $K$-theories

Hengda Bao·Xiaoman Chen·Jiawen Zhang
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Abstract

In this paper, we introduce a notion of strongly quasi-local algebras. They are defined for each discrete metric space with bounded geometry, and sit between the Roe algebra and the quasi-local algebra. We show that strongly quasi-local algebras are coarse invariants, hence encoding coarse geometric information of the underlying spaces. We prove that for a discrete metric space with bounded geometry which admits a coarse embedding into a Hilbert space, the inclusion of the Roe algebra into the strongly quasi-local algebra induces an isomorphism in $K$-theory.

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Hengda Bao, Xiaoman Chen, Jiawen Zhang. 2021-08-02. Strongly Quasi-local algebras and their $K$-theories. https://arxiv.org/abs/2108.00642

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