Strong shortcuts, generating sets, and isometric circles in asymptotic cones
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917819737702400 |
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| author | Hoda, Nima Riley, Timothy |
| author_facet | Hoda, Nima Riley, Timothy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21482 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong shortcuts, generating sets, and isometric circles in asymptotic cones Hoda, Nima Riley, Timothy Group Theory 20F65, 20F67, 20F69 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. |
| title | Strong shortcuts, generating sets, and isometric circles in asymptotic cones |
| topic | Group Theory 20F65, 20F67, 20F69 |
| url | https://arxiv.org/abs/2410.21482 |