Boundaries of Dehn fillings
Boundaries of Dehn fillings
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Dehn 填充物的边界
作者：
D. Groves;J. Manning;A. Sisto
我们开始研究 Dehn 填充操作下鲍迪奇边界和格罗莫夫边界的行为。特别地，我们展示了具有 2-球体边界的相对双曲群的许多 Dehn 填充是具有 2-球体边界的双曲。作为一个应用，我们证明坎农猜想隐含着坎农猜想的相对双曲版本。
We begin an investigation into the behavior of Bowditch and Gromov boundaries under the operation of Dehn filling. In particular we show many Dehn fillings of a toral relatively hyperbolic group with 2-sphere boundary are hyperbolic with 2-sphere boundary. As an application, we show that the Cannon conjecture implies a relatively hyperbolic version of the Cannon conjecture.