Finitely Presented Groups Acting on Trees
M. J. Dunwoody

TL;DR
The paper demonstrates that finitely presented groups acting on -trees can be decomposed into graphs of groups, and non-trivial actions lead to actions on simplicial -trees, advancing understanding of group actions on trees.
Contribution
It establishes a decomposition of finitely presented groups acting on -trees into graphs of groups, linking group actions to tree structures.
Findings
Any action of a finitely presented group on an -tree can be decomposed into a graph of groups.
Non-trivial actions on -trees imply the existence of actions on simplicial -trees.
Provides a structural understanding of finitely presented groups acting on -trees.
Abstract
It is shown that for any action of a finitely presented group on an -tree, there is a decomposition of as the fundamental group of a graph of groups related to this action. If the action of on is non-trivial, i.e. there is no global fixed point, then has a non-trivial action on a simplcial -tree.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Finite Group Theory Research
