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We describe a flexible construction that produces triples of finitely generated, residually finite groups M↪P↪Γ, where the maps induce isomorphisms of profinite completions M^≅ P^≅ Γ^, 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 F ∞. 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.
Bridson, Martin R 1
@article{10_2140_agt_2024_24_4103,
author = {Bridson, Martin R},
title = {Profinite isomorphisms and fixed-point properties},
journal = {Algebraic and Geometric Topology},
pages = {4103--4114},
publisher = {mathdoc},
volume = {24},
number = {7},
year = {2024},
doi = {10.2140/agt.2024.24.4103},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.4103/}
}
TY - JOUR AU - Bridson, Martin R TI - Profinite isomorphisms and fixed-point properties JO - Algebraic and Geometric Topology PY - 2024 SP - 4103 EP - 4114 VL - 24 IS - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.4103/ DO - 10.2140/agt.2024.24.4103 ID - 10_2140_agt_2024_24_4103 ER -
Bridson, Martin R. Profinite isomorphisms and fixed-point properties. Algebraic and Geometric Topology, Tome 24 (2024) no. 7, pp. 4103-4114. doi: 10.2140/agt.2024.24.4103
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