S. O. Rourke

activity

20112020

most citedAffine actions on non-archimedean trees

3 citations · 3 across the 3 of their papers we have counts for

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4 papers · 1 filter

math.GR2020

Affine structures, wreath products and free affine actions on linear non-archimedean trees

Shane O Rourke

Let $Λ$ be an ordered abelian group, $Aut^{+} (Λ)$ the group of order-preserving automorphisms of $Λ$ , $G$ a group and $α : G \to Aut^{+} (Λ)$ a homomorphism. An $α$ -affine…

math.GR2015

A combination theorem for affine tree-free groups

Shane O Rourke

Let $Λ_{0}$ be an ordered abelian group. We show how an $ATF (Z \times Λ_{0})$ group -- that is, a group admitting a free affine action without inversions on a $\mathbb{…

math.GR2012

A tree-free group that is not orderable

Shane O. Rourke

I. M. Chiswell has asked whether every group that admits a free isometric action (without inversions) on a $Λ$ -tree is orderable. We give an example of a multiple HNN extension $Γ$ …

math.GR2011★ 3 cited

Affine actions on non-archimedean trees

Shane O Rourke

We initiate the study of affine actions of groups on $Λ$ -trees for a general ordered abelian group $Λ$ ; these are actions by dilations rather than isometries. This gives a common g…