Some 3-manifold groups with the same finite quotients
By J. Hempel. 2014
46 citations recorded by the source corpus.
We give examples of closed, oriented 3-manifolds whose fundamental groups are not isomorphic, but yet have the same sets of finite quotient groups; hence the same profinite completions. We also give examples of compact, oriented 3-manifolds with non-empty boundaries whose fundamental groups though isomorphic have distinct peripheral structures, but yet have the same sets of finite peripheral pair quotients (defined below). The examples are Seifert Fibered Spaces with zero rational Euler number; moreover most of these manifolds give rise to such examples.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/57a86757598260ddffd9b33652fb2fd57aeb58a5
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Distinguishing geometries using finite quotients (2014, methodology): “Funar [9] used work of Stebe [46] to exhibit Sol manifolds that answer the Calegari– Freedman–Walker question in the negative, and more recently Hempel [21] has exhibited Seifert fibred examples.”
- Profinite rigidity for Seifert fibre spaces (2015, background): “But B is a good group, hence H(2)(B̂;Z/t) is canonically isomorphic to H(2)(B;Z/t); and ζG, ζG′ are the images of ηG, ηG′ under the maps H(2)(B;Z)→ H(2)(B;Z/t) ∼= H(2)(B̂;Z/t) It remains to show that no automorphisms of B̂ and Z/t can carry ζG to ζG′ under the induced maps on H(2)(B̂;Z/t) for all t ”