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arXiv · 2410.21482

Strong shortcuts, generating sets, and isometric circles in asymptotic cones

Nima Hoda·Timothy Riley
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Abstract

We show that whether loops can be shortcut in a group's Cayley graph depends on the choice of finite generating set. Our example is the direct product of two rank-2 free groups and a consequence is that this group has asymptotic cones with isometrically embedded circles that are null-homotopic.

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Nima Hoda, Timothy Riley. 2024-10-28. Strong shortcuts, generating sets, and isometric circles in asymptotic cones. https://arxiv.org/abs/2410.21482

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