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The approach reveals a minimal action of the mapping class group on a newly defined boundary, indicating its structure and properties.
We construct a boundary for the mapping class group Mod(S) of a surface S of finite type. The action of Mod(S) on this boundary is minimal, strongly proximal and topologically free. The boundary is the boundary of a Z-structure for any torsion free finite index subgroup of Mod(S).
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Ursula Hamenstädt (2025) studied this question.
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