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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