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Strong shortcuts, generating sets, and isometric circles in asymptotic cones
Published 28 Oct 2024 in math.GR | (2410.21482v1)
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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