Strong shortcuts, generating sets, and isometric circles in asymptotic cones
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.
Authors
- Nima Hoda (ORCID: https://orcid.org/0000-0002-6308-7751)
- Tim Riley (ORCID: https://orcid.org/0009-0004-3699-0322)
Institutions
- Cornell University (US)
Publication Details
- Journal
- Proceedings of the American Mathematical Society
- Published
- 2025-11-25
- DOI
- https://doi.org/10.1090/proc/17451
- Primary Topic
- Mathematics and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00