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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| Format: | Journal article |
| Jezik: | English |
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Mathematical Sciences Publishers
2024
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| _version_ | 1826316854136668160 |
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| author | Bridson, M |
| author_facet | Bridson, M |
| author_sort | Bridson, M |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T08:10:34Z |
| format | Journal article |
| id | oxford-uuid:13f4df2b-b0c0-4cc2-ab9f-c4bbd4b6647f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-02-19T04:29:25Z |
| publishDate | 2024 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | oxford-uuid:13f4df2b-b0c0-4cc2-ab9f-c4bbd4b6647f2024-12-20T09:04:53ZProfinite isomorphisms and fixed-point propertiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:13f4df2b-b0c0-4cc2-ab9f-c4bbd4b6647fEnglishSymplectic ElementsMathematical Sciences Publishers2024Bridson, MWe 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. |
| spellingShingle | Bridson, M Profinite isomorphisms and fixed-point properties |
| title | Profinite isomorphisms and fixed-point properties |
| title_full | Profinite isomorphisms and fixed-point properties |
| title_fullStr | Profinite isomorphisms and fixed-point properties |
| title_full_unstemmed | Profinite isomorphisms and fixed-point properties |
| title_short | Profinite isomorphisms and fixed-point properties |
| title_sort | profinite isomorphisms and fixed point properties |
| work_keys_str_mv | AT bridsonm profiniteisomorphismsandfixedpointproperties |