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arXiv · 2402.16335

Transfinite Extension of Nuclear Dimension

Jingming Zhu·Jiawen Zhang
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Abstract

In this paper, we introduce a notion of transfinite nuclear dimension for $C^*$-algebras, which coincides with the nuclear dimension when taking values in natural numbers. We use it to characterise a stronger form of having nuclear dimension at most $\omega$ and moreover, we show that the transfinite nuclear dimension of a uniform Roe algebra is bounded by the transfinite asymptotic dimension of the underlying space. Hence we obtain that the uniform Roe algebra for spaces with asymptotic property C has the corona factorisation property.

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Jingming Zhu, Jiawen Zhang. 2024-02-26. Transfinite Extension of Nuclear Dimension. https://arxiv.org/abs/2402.16335

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