Profinite isomorphisms and fixed-point properties
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908165182849024 |
|---|---|
| author | Bridson, Martin R. |
| author_facet | Bridson, Martin R. |
| contents | We describe a flexible construction that produces triples of finitely generated, residually finite groups $M\hookrightarrow P \hookrightarrow Γ$, where the maps induce isomorphisms of profinite completions $\widehat{M}\cong\widehat{P}\cong\widehatΓ$, but $M$ and $Γ$ have Serre's property FA while $P$ does not. In this construction, $P$ is finitely presented and $Γ$ is of type ${\rm{F}}_\infty$. 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 CAT$(0)$ space of dimension at most $d$, while $P$ acts without a fixed point on a tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02357 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Profinite isomorphisms and fixed-point properties Bridson, Martin R. Group Theory 20F67, 20J05, (20E08, 20E18) We describe a flexible construction that produces triples of finitely generated, residually finite groups $M\hookrightarrow P \hookrightarrow Γ$, where the maps induce isomorphisms of profinite completions $\widehat{M}\cong\widehat{P}\cong\widehatΓ$, but $M$ and $Γ$ have Serre's property FA while $P$ does not. In this construction, $P$ is finitely presented and $Γ$ is of type ${\rm{F}}_\infty$. 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 CAT$(0)$ space of dimension at most $d$, while $P$ acts without a fixed point on a tree. |
| title | Profinite isomorphisms and fixed-point properties |
| topic | Group Theory 20F67, 20J05, (20E08, 20E18) |
| url | https://arxiv.org/abs/2304.02357 |