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

Martin R. Bridson

Displaying similar documents to “The rhombic dodecahedron and semisimple actions of Aut(Fₙ) on CAT(0) spaces”

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Rakhimov, A.A. (2004)

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Ana Agore, Gigel Militaru (2012)

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We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups (H;G; α; β) is deformed using a combinatorial datum (σ; v; r) consisting of an automorphism σ of H, a permutation v of the set G and a transition map r: G → H in order to obtain a new matched pair (H; (G; *); α′, β′) such that there exists a σ-invariant isomorphism of groups H α⋈β G ≅H α′⋈β′ (G, *). Moreover, if we fix the group H and the automorphism σ...

Amenable, transitive and faithful actions of groups acting on trees

Pierre Fima (2014)

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We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such an action exists if the initial groups admit an amenable and almost free action with infinite orbits (e.g. virtually free groups or infinite amenable groups). Our result relies on the Baire category Theorem. We extend the result to groups acting on trees.

Structure and Regidity in Hyperbolic Groups. I.

E. Rips, Z. Sela (1994)

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Amenable actions of nonamenable groups.

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Bernhard Leeb, Michael Kapovich (1996)

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Finite-finitary, polycyclic-finitary and Chernikov-finitary automorphism groups

B. A. F. Wehrfritz (2015)

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If X is a property or a class of groups, an automorphism ϕ of a group G is X-finitary if there is a normal subgroup N of G centralized by ϕ such that G/N is an X-group. Groups of such automorphisms for G a module over some ring have been very extensively studied over many years. However, for groups in general almost nothing seems to have been done. In 2009 V. V. Belyaev and D. A. Shved considered the general case for X the class of finite groups. Here we look further at the finite case...

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R. Patrick Martineau (1973)

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A - finite actions and their automorphism groups.

S. Rankin, C. Reis (1982)

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Alessandra Guazzi, Mattia Mecchia, Bruno Zimmermann (2011)

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We consider finite groups which admit a faithful, smooth action on an acyclic manifold of dimension three, four or five (e.g. Euclidean space). Our first main result states that a finite group acting on an acyclic 3- or 4-manifold is isomorphic to a subgroup of the orthogonal group O(3) or O(4), respectively. The analogous statement remains open in dimension five (where it is not true for arbitrary continuous actions, however). We prove that the only finite nonabelian simple groups admitting...

Semisimple extensions of irrational rotations

Mariusz Lemańczyk, Mieczysław K. Mentzen, Hitoshi Nakada (2003)

Studia Mathematica

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We show that semisimple actions of l.c.s.c. Abelian groups and cocycles with values in such groups can be used to build new examples of semisimple automorphisms (ℤ-actions) which are relatively weakly mixing extensions of irrational rotations.