Finite abelian subgroups of the mapping class group

DOI10.2140/agt.2007.7.1651zbMath1126.14038arXivmath/0611650OpenAlexW3101890239MaRDI QIDQ2464928

Aaron Wootton, S. Allen Broughton

Publication date: 18 December 2007

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611650

zbMATH Keywords

automorphism groups of surfacesfinite subgroups of mapping class groups

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Coverings of curves, fundamental group (14H30) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Automorphisms of curves (14H37) Automorphisms of surfaces and higher-dimensional varieties (14J50)

Related Items (12)

Split metacyclic actions on surfaces ⋮ Enumerating quasiplatonic cyclic group actions ⋮ Geometric realizations of cyclic actions on surfaces. II ⋮ A lower bound for the number of group actions on a compact Riemann surface ⋮ Uniqueness of orientation-preserving free actions of finite abelian groups on surfaces ⋮ Commuting conjugates of finite-order mapping classes ⋮ Non-abelian simple groups act with almost all signatures ⋮ On the connectedness of the branch locus of the moduli space of Riemann surfaces of low genus ⋮ A lower bound for the number of finitely maximal 𝐶_{𝑝}-actions on a compact oriented surface ⋮ Maximal group actions on compact oriented surfaces ⋮ Topologically unique maximal elementary Abelian group actions on compact oriented surfaces ⋮ On the orbifold structure of the moduli space of Riemann surfaces of genera four and five

Uses Software

• GAP
• Magma
• Maple

Cites Work

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• A survey of the Torelli group
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• Automorphisms of Maps, Permutation Groups and Riemann Surfaces
• CYCLIC GROUPS OF AUTOMORPHISMS OF A COMPACT RIEMANN SURFACE
• Abelian Groups of Automorphisms of Compact Riemann Surfaces
• The Classification of Non-Euclidean Plane Crystallographic Groups
• Subgroups of Fuchsian Groups and Finite Permutation Groups
• On Branch Loci in Teichmuller Space
• Modulus Space is Simply-Connected
• Finitely Maximal Fuchsian Groups
• The Nielsen realization problem

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