Displaying similar documents to “On finite groups acting on acyclic low-dimensional manifolds”

The rhombic dodecahedron and semisimple actions of Aut(Fₙ) on CAT(0) spaces

Martin R. Bridson (2011)

Fundamenta Mathematicae

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We consider actions of automorphism groups of free groups by semisimple isometries on complete CAT(0) spaces. If n ≥ 4 then each of the Nielsen generators of Aut(Fₙ) has a fixed point. If n = 3 then either each of the Nielsen generators has a fixed point, or else they are hyperbolic and each Nielsen-generated ℤ⁴ ⊂ Aut(F₃) leaves invariant an isometrically embedded copy of Euclidean 3-space 𝔼³ ↪ X on which it acts as a discrete group of translations with the rhombic dodecahedron...

Orderable 3-manifold groups

Steven Boyer, Dale Rolfsen, Bert Wiest (2005)

Annales de l’institut Fourier

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We investigate the orderability properties of fundamental groups of 3-dimensional manifolds. Many 3-manifold groups support left-invariant orderings, including all compact P 2 -irreducible manifolds with positive first Betti number. For seven of the eight geometries (excluding hyperbolic) we are able to characterize which manifolds’ groups support a left-invariant or bi-invariant ordering. We also show that manifolds modelled on these geometries have virtually bi-orderable groups. The question...