Mapping class factorization via fatgraph Nielsen reduction

zbMath1242.57012arXiv0904.4067MaRDI QIDQ663534

Alex James Bene

Publication date: 17 February 2012

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.4067

zbMATH Keywords

mapping class groupgroupoidWhitehead moves

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) General low-dimensional topology (57M99) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Other groups related to topology or analysis (20F38) Special aspects of infinite or finite groups (20F99) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Cancellation theory of groups; application of van Kampen diagrams (20F06)

Cites Work

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• A chord diagrammatic presentation of the mapping class group of a once bordered surface
• Canonical extensions of the Johnson homomorphisms to the Torelli groupoid
• Groupoid extensions of mapping class representations for bordered surfaces
• The virtual cohomological dimension of the mapping class group of an orientable surface
• The decorated Teichmüller space of punctured surfaces
• Decorated Teichmüller theory of bordered surfaces
• Universal constructions in Teichmüller theory
• Torelli groups, extended Johnson homomorphisms, and new cycles on the moduli space of curves
• Mapping class groups are automatic

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