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Investigation characterizes group compactifications and establishes retraction theorems for hyperbolic groups.
We characterize group compactifications of discrete groups for which there exists an equivariant retraction onto the boundary. In particular, we prove an equivariant analogue of Brouwer's No-Retraction theorem for large classes of group compactifications, which includes actions of hyperbolic groups on their Gromov boundary.
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Hartman et al. (2025) studied this question.
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