Group actions on trees furnish a unified geometric way of recasting the chapter of combinatorial group theory dealing with free groups, amalgams, and HNN extensions. Some of the principal examples arise from rank one simple Lie groups over a non-archimidean local field acting on their Bruhat-Tits trees. In particular this leads to a powerful method for studying lattices in such Lie groups.
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Group actions on trees furnish a unified geometric way of recasting the chapter of combinatorial group theory dealing with free groups, amalgams, and HNN extensions. Some of the principal examples arise from rank one simple Lie groups over a non-archimidean local field acting on their Bruhat-Tits trees. In particular this leads to a powerful method for studying lattices in such Lie groups.
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