Dehn fillings and elementary splittings

Abstract

We consider conditions on relatively hyperbolic groups about the non-existence of certain kinds of splittings, and show these properties persist in long Dehn fillings. We deduce that certain connectivity properties of the Bowditch boundary persist under long fillings.

44 pages, 1 figure. v2 minor changes and corrections. v3 corrected Corollary 4.6; this version accepted for publication in Transactions of the AMS