Displaying similar documents to “Free group automorphisms, invariant orderings and topological applications.”

On generalized M * - groups.

Ikikardes, Sebahattin, Sahin, Recep (2010)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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On the dynamics of (left) orderable groups

Andrés Navas (2010)

Annales de l’institut Fourier

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We develop dynamical methods for studying left-orderable groups as well as the spaces of orderings associated to them. We give new and elementary proofs of theorems by Linnell (if a left-orderable group has infinitely many orderings, then it has uncountably many) and McCleary (the space of orderings of the free group is a Cantor set). We show that this last result also holds for countable torsion-free nilpotent groups which are not rank-one Abelian. Finally, we apply our methods to the...

Fox pairings and generalized Dehn twists

Gwénaël Massuyeau, Vladimir Turaev (2013)

Annales de l’institut Fourier

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We introduce a notion of a Fox pairing in a group algebra and use Fox pairings to define automorphisms of the Malcev completions of groups. These automorphisms generalize to the algebraic setting the action of the Dehn twists in the group algebras of the fundamental groups of surfaces. This work is inspired by the Kawazumi–Kuno generalization of the Dehn twists to non-simple closed curves on surfaces.

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...