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arXiv · 2310.09369

Coarse embeddings of quotients by finite group actions

Thomas Weighill
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Abstract

We prove that for a metric space $X$ and a finite group $G$ acting on $X$ by isometries, if $X$ coarsely embeds into a Hilbert space, then so does the quotient $X/G$. A crucial step towards our main result is to show that for any integer $k > 0$ the space of unordered $k$-tuples of points in Hilbert space, with the $1$-Wasserstein distance, itself coarsely embeds into Hilbert space. Our proof relies on establishing bounds on the sliced Wasserstein distance between empirical measures in $\mathbb{R}^n$.

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Thomas Weighill. 2023-10-13. Coarse embeddings of quotients by finite group actions. https://arxiv.org/abs/2310.09369

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