# 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}
}
• Published 18 September 2009
• Mathematics
• Journal of Topology and Analysis
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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