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arXiv · 2508.11065

The arc complex is not quasi-isometric to the sphere complex

Tarik Aougab·Marissa Loving
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Abstract

We show that the arc complex $\mathcal{A}(S_{g,1})$ is not quasi-isometric to the sphere complex $\mathcal S_{2g}$ associated to the double of a genus $2g$ handlebody. Along the way, we present a simple proof that $\mathcal{A}(S_{g,1})$ is quasi-isometrically rigid.

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Tarik Aougab, Marissa Loving. 2025-08-14. The arc complex is not quasi-isometric to the sphere complex. https://arxiv.org/abs/2508.11065

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