Anti-tori in square complex groups
| dc.creator | Rattaggi, Diego | |
| dc.date | 2004-11-24 | |
| dc.date | 2005-07-21 | |
| dc.date.accessioned | 2026-07-07T05:14:39Z | |
| dc.date.available | 2026-07-07T05:14:39Z | |
| dc.description | An anti-torus is a subgroup $<a,b>$ in the fundamental group of a compact non-positively curved space $X$, acting in a specific way on the universal covering space $\tilde{X}$ such that $a$ and $b$ do not have any commuting non-trivial powers. We construct and investigate anti-tori in a class of commutative transitive fundamental groups of finite square complexes, in particular for the groups $Γ_{p,l}$ originally studied by Mozes [15]. It turns out that anti-tori in $Γ_{p,l}$ directly correspond to non-commuting pairs of Hamilton quaternions. Moreover, free anti-tori in $Γ_{p,l}$ are related to free groups generated by two integer quaternions, and also to free subgroups of $\mathrm{SO}_3(\mathbb{Q})$. As an application, we prove that the multiplicative group generated by the two quaternions $1+2i$ and $1+4k$ is not free. | |
| dc.description | 16 pages, some minor changes, this is the final version | |
| dc.identifier | https://arxiv.org/abs/math/0411547 | |
| dc.identifier | http://arxiv.org/abs/math/0411547 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73360 | |
| dc.subject | Group Theory | |
| dc.subject | Rings and Algebras | |
| dc.title | Anti-tori in square complex groups | |
| dc.type | text |