THE BRAID GROUP $B_{n,m}(\mathbb{S}^{2})$ AND A GENERALISATION OF THE FADELL–NEUWIRTH SHORT EXACT SEQUENCE

DOI10.1142/S0218216505003841zbMath1072.55013MaRDI QIDQ5462715

John Guaschi, Daciberg Lima Gonçalves

Publication date: 3 August 2005

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

zbMATH Keywords

configuration space2-spherebraid groupcross-sectionFadell-Neuwirth short exact sequencecolored braids

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Discriminantal varieties and configuration spaces in algebraic topology (55R80) Fiber spaces in algebraic topology (55R05)

Related Items

The quaternion group as a subgroup of the sphere braid groups ⋮ Lower central series, surface braid groups, surjections and permutations ⋮ The braid group \(B_{n, m}(\mathbb{R} P^2)\) and the splitting problem of the generalised Fadell-Neuwirth short exact sequence ⋮ THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE ⋮ Section problems for configurations of points on the Riemann sphere ⋮ A survey of the homotopy properties of inclusion of certain types of configuration spaces into the Cartesian product ⋮ Fixed points of \(n\)-valued maps, the fixed point property and the case of surfaces -- a braid approach ⋮ The Borsuk-Ulam theorem for \(n\)-valued maps between surfaces ⋮ Minimal generating and normally generating sets for the braid and mapping class groups of \(\mathbb D^2\), \(\mathbb S^2\) and \(\mathbb RP^2\). ⋮ ABELIAN AND METABELIAN QUOTIENT GROUPS OF SURFACE BRAID GROUPS ⋮ The classification and the conjugacy classes of the finite subgroups of the sphere braid groups. ⋮ Wecken homotopies ⋮ Section problems for configuration spaces of surfaces ⋮ The Borsuk-Ulam theorem for maps into a surface ⋮ Braids, their Properties and Generalizations ⋮ The lower central and derived series of the braid groups of the sphere ⋮ Symplectic (-2)-spheres and the symplectomorphism group

Cites Work

• Some subgroups of Artin's braid group
• The braid groups of the projective plane.
• Homotopy groups of configuration spaces and the string problem of Dirac
• The braid groups of \(E^ 2\) and \(S^ 2\)
• Theory of braids
• Braids and permutations
• On loop spaces of configuration spaces
• The roots of the full twist for surface braid groups
• Configuration Spaces.
• The Braid Groups.
• On the structure of surface pure braid groups.