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arXiv · 2511.22438

$K$-theory of ghostly ideals for $\ell^p$-coarsely embeddable spaces

Liang Guo·Kang Li·Qin Wang
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Abstract

Ghostly ideals are among the most mysterious objects in coarse index theory. In this paper, we show that if a metric space $X$ with bounded geometry admits a coarse embedding into an $\ell^p$-space ($1 \le p < \infty$), then the canonical inclusion from any geometric ideal to the corresponding ghostly ideal induces an isomorphism in $K$-theory. As consequences, we deduce that such spaces satisfy the relative coarse Baum-Connes conjectures, as well as the operator norm localization property for finite rank projections ($ONL_{\mathcal P_{Fin}}$).

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Liang Guo, Kang Li, Qin Wang. 2025-11-27. $K$-theory of ghostly ideals for $\ell^p$-coarsely embeddable spaces. https://arxiv.org/abs/2511.22438

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