# C$^*$-simple groups: amalgamated free products, HNN extensions, and fundamental groups of 3-manifolds

@article{Harpe2009CsimpleGA, title={C\$^*\$-simple groups: amalgamated free products, HNN extensions, and fundamental groups of 3-manifolds}, author={Pierre de la Harpe and Jean-Philippe Pr'eaux}, journal={Journal of Topology and Analysis}, year={2009}, volume={03}, pages={451-489} }

We establish sufficient conditions for the C*-simplicity of two classes of groups. The first class is that of groups acting on trees, such as amalgamated free products, HNN-extensions, and their nontrivial subnormal subgroups; for example normal subgroups of Baumslag–Solitar groups. The second class is that of fundamental groups of compact 3-manifolds, related to the first class by their Kneser–Milnor and JSJ decompositions. Much of our analysis deals with conditions on an action of a group…

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