Minimal generating and normally generating sets for the braid and mapping class groups of \(\mathbb D^2\), \(\mathbb S^2\) and \(\mathbb RP^2\).

DOI10.1007/s00209-012-1090-0zbMath1275.20033arXiv1201.6482OpenAlexW3122102773MaRDI QIDQ1955724

Daciberg Lima Gonçalves, John Guaschi

Publication date: 18 June 2013

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.6482

zbMATH Keywords

numbers of conjugacy classespure braid groupsmapping class groupsbraids on surfacesnormal generating sets

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Generators, relations, and presentations of groups (20F05) Braid groups; Artin groups (20F36) Topological methods in group theory (57M07)

Related Items

Lower central series, surface braid groups, surjections and permutations, Crystallographic groups and flat manifolds from surface braid groups, Symplectic (-2)-spheres and the symplectomorphism group

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stable classical groups and strongly torsion generated groups.
• Über Automorphismen von Fundamentalgruppen berandeter Flächen
• The braid groups of the projective plane.
• The integral cohomology algebras of ordered configuration spaces of spheres
• The braid groups of the projective plane and the Fadell-Neuwirth short exact sequence.
• Homology and central series of groups
• The braid groups of \(E^ 2\) and \(S^ 2\)
• Theory of braids
• On loop spaces of configuration spaces
• Surface braid groups and coverings
• Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane
• Seifert Fibre Spaces and Braid Groups
• Strongly torsion generated groups
• On the structure of the centralizer of a braid
• Sur les transformations périodiques de la surface de sphère
• The roots of the full twist for surface braid groups
• The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups
• THE BRAID GROUP $B_{n,m}(\mathbb{S}^{2})$ AND A GENERALISATION OF THE FADELL–NEUWIRTH SHORT EXACT SEQUENCE
• Braid Groups of Compact 2-Manifolds with Elements of Finite Order
• Mapping class groups and their relationship to braid groups
• The Word Problem and Consequences for the Braid Groups and Mapping Class Groups of the 2-Sphere
• The Braid Groups.