Group actions on dendrites and curves

Abstract

We establish obstructions for groups to act by homeomorphisms on dendrites. For instance, lattices in higher rank simple Lie groups will always fix a point or a pair. The same holds for irreducible lattices in products of connected groups. Further results include a Tits alternative and a description of the topological dynamics. We briefly discuss to what extent our results hold for more general topological curves.

minor additions to v2

References in corpus (5)

• Boundaries, rigidity of representations, and Lyapunov exponents
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• Structural properties of dendrite groups
• An extension criterion for lattice actions on the circle
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Cited by in corpus (8)

• Group actions on treelike compact spaces
• Topological properties of Wazewski dendrite groups
• Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms
• A group with Property (T) acting on the circle
• A note on actions with finite orbits on dendrites
• Some examples of tame dynamical systems answering questions of Glasner and Megrelishvili
• On Thompson Groups for Ważewski Dendrites
• Rigidity of matrix group actions on CAT(0) spaces with possible parabolic isometries and uniquely arcwise connected spaces