Two-generator subgroups of the pure braid group.

DOI10.1007/s10711-009-9440-8zbMath1213.20035arXiv0812.1783OpenAlexW2159084360MaRDI QIDQ5961887

Christopher J. Leininger, Dan Margalit

Publication date: 16 September 2010

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.1783

zbMATH Keywords

pure braid groupsfree groupsmapping class groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Braid groups; Artin groups (20F36) General geometric structures on low-dimensional manifolds (57M50)

Related Items

Automorphism group of the commutator subgroup of the braid group, Commensurability invariance for abelian splittings of right-angled Artin groups, braid groups and loop braid groups, Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents, Subgroups generated by two Dehn twists on a nonorientable surface

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniform independence in linear groups.
• Two-generated groups acting on trees
• The structure of subgroup of mapping class groups generated by two Dehn twists
• On complexity of the word problem in braid groups and mapping class groups
• Normal all pseudo-Anosov subgroups of mapping class groups
• Groups generated by positive multi-twists and the fake lantern problem
• Uniform uniform exponential growth of subgroups of the mapping class group
• Theory of braids
• Trees and mapping class groups
• A "Tits-Alternative" for Subgroups of Surface Mapping Class Groups
• On the geometry and dynamics of diffeomorphisms of surfaces
• Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents
• Mapping class groups and their relationship to braid groups
• Presentations for the punctured mapping class groups in terms of Artin groups