Configurations, braids, and homotopy groups

DOI10.1090/S0894-0347-05-00507-2zbMath1188.55007MaRDI QIDQ3376936

A. J. Berrick, Yan Loi Wong, Jie Wu, Frederick R. Cohen

Publication date: 27 March 2006

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

braid groupsconfiguration spaceMoore complexhomotopy groups of spheresBrunnian braidscrossed simplicial group

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Topological methods in group theory (57M07) General geometric structures on low-dimensional manifolds (57M50) Simplicial sets and complexes in algebraic topology (55U10) Derived series, central series, and generalizations for groups (20F14) Homotopy groups of spheres (55Q40)

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Cites Work

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• Simplicial group models for \(\Omega ^ nS^ nX\)
• On the suspension sequence
• The geometric realization of a semi-simplicial complex
• A combinatorial definition of homotopy groups
• A simplicial group construction for balanced products
• The lower central series of a fiber-type arrangement
• Integral invariants of 3-manifolds
• Links of Brunnian type
• A decomposition of \(\pi^*(S^{2p+1};Z/pZ)\)
• \(\Gamma^+\)-structures. III: The stable structure of \(\Omega^\infty\Sigma^\infty A\)
• Nonpositive curvature of blow-ups
• On fibrewise simplicial monoids and Milnor-Carlsson's constructions
• A compactification of configuration spaces
• Elliptic KZ system, braid group of the torus and Vassiliev invariants
• The Lie algebra of the pure braid group
• Normal all pseudo-Anosov subgroups of mapping class groups
• On Borromean links
• Homotopy invariant algebraic structures on topological spaces
• Configuration spaces and Vassiliev classes in any dimension
• The integral cohomology algebras of ordered configuration spaces of spheres
• The mod-\(p\) lower central series and the Adams spectral sequence
• Homotopical algebra
• Generalized Brunnian links
• Über die Topologie der Gruppen-Mannigfaltigkeiten und ihre Verallgemeinerungen
• Theory of braids
• The algebraical braid group
• Homologie singulière des espaces fibrés. Applications
• Combinatorial descriptions of homotopy groups of certain spaces
• ARTIN'S BRAID GROUPS, FREE GROUPS, AND THE LOOP SPACE OF THE 2-SPHERE
• A BRAIDED SIMPLICIAL GROUP
• Compositional Methods in Homotopy Groups of Spheres. (AM-49)
• Mapping class groups of low genus and their cohomology
• Crossed Simplicial Groups and their Associated Homology
• Intersection Theory of Moduli Space of Stable N-Pointed Curves of Genus Zero
• Differential Topology
• On natural coalgebra decompositions of tensor algebras and loop suspensions
• Towards a characterization of smooth braids
• A Contribution to the Theory of Groups of Prime-Power Order
• Decomposable Braids and Linkages
• Configuration Spaces.
• The Word Problem and Consequences for the Braid Groups and Mapping Class Groups of the 2-Sphere
• A Spectral Sequence for the Homotopy of Nice Spaces
• Braid groups are linear
• Braid groups are linear
• Simplicial homotopy theory
• Brunnian links are determined by their complements