Profinite and pro-𝑝 completions of Poincaré duality groups of dimension 3

DOI10.1090/S0002-9947-07-04519-9zbMath1143.20016OpenAlexW1996687701MaRDI QIDQ5437621

Dessislava H. Kochloukova, Pavel A. Zalesskii

Publication date: 21 January 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-07-04519-9

zbMATH Keywords

Euler characteristicsprofinite completionsdeficiencyPoincaré duality groupshomological invariantspro-\(p\) completions

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Homological methods in group theory (20J05) Limits, profinite groups (20E18) Poincaré duality spaces (57P10)

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Profinite completions of orientable Poincaré duality groups of dimension four and Euler characteristic zero. ⋮ Homological properties of abstract and profinite modules and groups. ⋮ Profinite extensions of centralizers and the profinite completion of limit groups ⋮ Recognition of being fibered for compact 3-manifolds ⋮ Normal subgroups of profinite groups of non-negative deficiency. ⋮ Pro-\(\mathcal {C}\) completions of orientable \(\mathrm{PD}^3\)-pairs ⋮ Cohomological goodness and the profinite completion of Bianchi groups. ⋮ Pro-\(p\) completions of Poincaré duality groups. ⋮ Profinite detection of 3-manifold decompositions ⋮ $3$-Manifold Groups are Virtually Residually $p$ ⋮ Groups with the same cohomology as their pro-\(p\) completions.

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