Geodesic
On the profinite distinguishability of hyperbolic Dehn fillings of finite-volume 3–manifolds
Rapoport, Paul1
1 Department of Mathematics, Temple University, Philadelphia, PA, United States
Algebraic and Geometric Topology, Tome 24 (2024) no. 9, pp. 4779-4797

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We use the Culler–Shalen machine and tools from model theory to study the profinite rigidity of residually finite groups, especially 3–manifold groups. We borrow a transfer principle from model theory to apply to ℂ–character varieties in order to study cofinite collections of 𝔽p–character varieties and prove that under certain finiteness conditions weaker than non-Hakenness, they all have the same (finite) cardinality. We prove that residually finite groups satisfying a niceness property are almost relatively profinitely distinguishable within a geometrically relevant class, and we finish up by applying that result to knot complements in S3 in particular.

DOI : 10.2140/agt.2024.24.4779
Keywords: geometric group theory, profinite, non-Haken, Dehn, filling, rigidity

Rapoport, Paul 1

1 Department of Mathematics, Temple University, Philadelphia, PA, United States 
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Rapoport, Paul. On the profinite distinguishability of hyperbolic Dehn fillings of finite-volume 3–manifolds. Algebraic and Geometric Topology, Tome 24 (2024) no. 9, pp. 4779-4797. doi: 10.2140/agt.2024.24.4779

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