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math.GR2024
Strong shortcuts, generating sets, and isometric circles in asymptotic cones
Nima Hoda, Timothy Riley
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…
math.GR2024
The quadric flat torus theorem
Nima Hoda, Zachary Munro
We prove a flat torus theorem for quadric complexes. In particular, we show that if a non-cyclic free abelian group acts metrically properly on a quadric complex , then $G \…