Map(S(n)) for infinite-genus surfaces with n ends is topologically generated by three or four torsion elements, with explicit counts and orders depending on n.
Torsion Elements in the Mapping Class Group of a Surface
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abstract
Given a finite set of $r$ points in a closed surface of genus $g$, we consider the torsion elements in the mapping class group of the surface leaving the finite set invariant. We show that the torsion elements generate the mapping class group if and only if $(g, r) \neq (2, 5k+4)$ for some integer $k$.
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math.GT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Small Torsion Topological Generators for Big Mapping Class Groups
Map(S(n)) for infinite-genus surfaces with n ends is topologically generated by three or four torsion elements, with explicit counts and orders depending on n.