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• W2743261966 endingPage "2836" @default.
• W2743261966 startingPage "2795" @default.
• W2743261966 abstract "In this paper we show that the existence of a non-parabolic local cut point in the Bowditch boundary $partial(G,mathbb{P})$ of a relatively hyperbolic group $(G,mathbb{P})$ implies that $G$ splits over a $2$-ended subgroup. This theorem generalizes a theorem of Bowditch from the setting of hyperbolic groups to relatively hyperbolic groups. As a consequence we are able to generalize a theorem of Kapovich and Kleiner by classifying the homeomorphism type of $1$-dimensional Bowditch boundaries of relatively hyperbolic groups which satisfy certain properties, such as no splittings over $2$-ended subgroups and no peripheral splittings. In order to prove the boundary classification result we require a notion of ends of a group which is more general than the standard notion. We show that if a finitely generated discrete group acts properly and cocompactly on two generalized Peano continua $X$ and $Y$, then $Ends(X)$ is homeomorphic to $Ends(Y)$. Thus we propose an alternate definition of $Ends(G)$ which increases the class of spaces on which $G$ can act." @default.
• W2743261966 created "2017-08-17" @default.
• W2743261966 creator A5058953866 @default.
• W2743261966 date "2019-10-20" @default.
• W2743261966 modified "2023-09-25" @default.
• W2743261966 title "Local cut points and splittings of relatively hyperbolic groups" @default.
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• W2743261966 doi "https://doi.org/10.2140/agt.2019.19.2795" @default.
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