Plane motion groups and virtual Poincaré duality of dimension two

DOI10.1007/BF01399508zbMath0501.20031OpenAlexW2081319795MaRDI QIDQ1172151

Heinz Müller, Beno Eckmann

Publication date: 1982

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142955

zbMATH Keywords

surface group2-dimensional Poincare-duality groupdecomposition theorems for group pairsfundamental group of closed surfaceHNN- extensionNielsen's realization problemplane motion groupsPoincare-duality group pairsvirtual surface group

Mathematics Subject Classification ID

Homological methods in group theory (20J05) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Other geometric groups, including crystallographic groups (20H15) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

Related Items (6)

Matrix Classes Realized by Automorphisms of Compact Riemann Surfaces of Genus Two ⋮ Dirichlet's energy on Teichmüller's moduli space and the Nielsen realization problem ⋮ Deficiency and commensurators ⋮ On 4-manifolds with universal covering space \(S^ 2\times R^ 2\) or \(S^ 3\times R\) ⋮ Homomorphisms of nonzero degree betweenPD_n-groups ⋮ Centralizers and normalizers of subgroups of \(\text{PD}_3\)-groups and open \(\text{PD}_3\)-groups.

Cites Work

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• Surfaces and planar discontinuous groups. Revised and expanded transl. from the German by J. Stillwell
• Poincaré duality groups of dimension two
• Decomposition theorems for group pairs
• On accessible groups
• A remark on subgroups of infinite index in Poincaré duality groups
• Almost finitely presented soluble groups
• Relative homology and Poincaré duality for group pairs
• Accessibility and Groups of Cohomological Dimension One
• The Nielsen realization problem

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