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- W3153163329 abstract "We prove that the fundamental group of a finite graph of convergence groups with parabolic edge groups is a convergence group. Using this result, under some mild assumptions, we prove a combination theorem for a graph of convergence groups with dynamically quasi-convex edge groups (Theorem 1.3). To prove these results, we use a modification of Dahmani’s technique [8]. Then we show that the fundamental group of a graph of relatively hyperbolic groups with edge groups either parabolic or infinite cyclic is relatively hyperbolic and construct Bowditch boundary. Finally, we show that the homeomorphism type of Bowditch boundary of the fundamental group of a graph of relatively hyperbolic groups with parabolic edge groups is determined by the homeomorphism type of the Bowditch boundaries of vertex groups (under some additional hypotheses) (Theorem 7.1). In the last section of the paper, we give some applications and examples." @default.
- W3153163329 created "2021-04-26" @default.
- W3153163329 creator A5089603239 @default.
- W3153163329 date "2022-07-27" @default.
- W3153163329 modified "2023-09-25" @default.
- W3153163329 title "Boundaries of graphs of relatively hyperbolic groups with cyclic edge groups" @default.
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- W3153163329 doi "https://doi.org/10.1007/s12044-022-00694-3" @default.
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