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arXiv · 2509.10072

Retraction Theorems for Group Compactifications

Yair Hartman·Aranka Hrušková·Mehrdad Kalantar·Tomer Zimhoni
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Abstract

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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Yair Hartman, Aranka Hrušková, Mehrdad Kalantar, Tomer Zimhoni. 2025-09-12. Retraction Theorems for Group Compactifications. https://arxiv.org/abs/2509.10072

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