Profinite isomorphisms and fixed-point properties
We describe a flexible construction that produces triples of finitely generated, residually finite groups M ãÑ P ãÑ Γ, where the maps induce isomorphisms of profinite completions Mx – Pp – Γ, but p M and Γ have Serre’s property FA while P does not. In this construction, P is finitely presented and Γ...
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| Formato: | Journal article |
| Idioma: | English |
| Publicado: |
Mathematical Sciences Publishers
2024
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| Summary: | We describe a flexible construction that produces triples
of finitely generated, residually finite groups M ãÑ P ãÑ Γ, where the
maps induce isomorphisms of profinite completions Mx – Pp – Γ, but p M
and Γ have Serre’s property FA while P does not. In this construction,
P is finitely presented and Γ is of type F8. More generally, given any
positive integer d, one can demand that M and Γ have a fixed point
whenever they act by semisimple isometries on a complete CATp0q space
of dimension at most d, while P acts without a fixed point on a tree. |
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