Relatively hyperbolic TDLC groups are closed under amalgams and HNN extensions over compact subgroups, and their Bowditch boundaries are determined by the boundaries of the vertex groups.
25, European Mathematical Society (EMS), Z\"urich, 2016, Winner of the 2016 EMS Monograph Award
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On combination theorems and Bowditch boundaries of relatively hyperbolic TDLC groups
Relatively hyperbolic TDLC groups are closed under amalgams and HNN extensions over compact subgroups, and their Bowditch boundaries are determined by the boundaries of the vertex groups.