Presentations for the punctured mapping class groups in terms of Artin groups

DOI10.2140/agt.2001.1.73zbMath0962.57008arXivmath/9911063OpenAlexW1980221109MaRDI QIDQ5927735

Luis Paris, Catherine Labruère

Publication date: 29 March 2001

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

Full work available at URL: https://arxiv.org/abs/math/9911063

Mathematics Subject Classification ID

General low-dimensional topology (57M99) Braid groups; Artin groups (20F36) Other groups related to topology or analysis (20F38)

Related Items

ACTION OF A GROTHENDIECK–TEICHMÜLLER GROUP ON TORSION ELEMENTS OF FULL TEICHMÜLLER MODULAR GROUPS OF GENUS ONE, The Zieschang–McCool method for generating algebraic mapping-class groups, Orbit equivalence rigidity of irreducible actions of right-angled Artin groups, Every mapping class group is generated by 6 involutions, Commensurability in Artin groups of spherical type, An infinite presentation for the mapping class group of a non-orientable surface with boundary, The complex of pant decompositions of a surface, Commensurability of geometric subgroups of mapping class groups, Generating the mapping class group of a nonorientable surface by crosscap transpositions, Automorphisms of the mapping class group of a nonorientable surface, HILDEN BRAID GROUPS, Dehn quandles of groups and orientable surfaces, The balanced superelliptic mapping class groups are generated by three elements, Broken Lefschetz fibrations, branched coverings, and braided surfaces, Computing equivalence classes of finite group actions on orientable surfaces, Surface framed braids., Non-isotopic symplectic surfaces in product 4-manifolds, Generating mapping class groups of nonorientable surfaces with boundary, Extending homeomorphisms from punctured surfaces to handlebodies., A finite presentation for the mapping class group of a nonorientable surface with Dehn twists and one crosscap slide as generators, A note on mapping class group actions on derived categories, A presentation for the mapping class group of a nonorientable surface, Symplectic surgeries along certain singularities and new Lefschetz fibrations, Two-generator subgroups of the pure braid group., Dehn twists have roots, Roots of Dehn twists on nonorientable surfaces, Artin groups of types \(F_4\) and \(H_4\) are not commensurable with that of type \(D_4\), Linearity of some low-complexity mapping class groups, An effective algebraic detection of the Nielsen–Thurston classification of mapping classes, Congruence subgroups of braid groups, The \(K(\pi,1)\)-conjecture implies the center conjecture for Artin groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A simple presentation for the mapping class group of an orientable surface
• Presentations for groups acting on simply-connected complexes
• The structure of the Torelli group. I: A finite set of generators for \({\mathcal I}\)
• Artin groups of finite type are biautomatic
• A presentation for the mapping class group of a closed orientable surface
• Planar graphs and presentations of braid groups
• On representations of Artin groups and the Tits conjecture
• Parabolic subgroups of Artin groups
• Geometric monodromy groups of simple singularities
• Artin groups and geometric monodromy
• A presentation of mapping class groups in terms of Artin groups and geometric monodromy of singularities
• Les immeubles des groupes de tresses généralises
• Artin-Gruppen und Coxeter-Gruppen
• Generalized Braid Groups and Mapping Class Gropus
• Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
• Geometric subgroups of mapping class groups
• Artin groups and the fundamental groups of some moduli spaces
• Mapping class groups and their relationship to braid groups
• A finite presentation of the mapping class group of a punctured surface