On loop spaces of configuration spaces

DOI10.1090/S0002-9947-02-02948-3zbMath0992.55006MaRDI QIDQ2781380

Frederick R. Cohen, Samuel Gitler

Publication date: 19 March 2002

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

zbMATH Keywords

decompositionsloop space homology

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Loop spaces (55P35) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Discriminantal varieties and configuration spaces in algebraic topology (55R80) Derived series, central series, and generalizations for groups (20F14)

Related Items (24)

The braid groups of the projective plane. ⋮ Rational homotopy type of the moduli of representations with Borel mold ⋮ Homotopy Lie algebras; lower central series and the Koszul property ⋮ Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence ⋮ Koszul spaces ⋮ THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE ⋮ Fixed points of \(n\)-valued maps, the fixed point property and the case of surfaces -- a braid approach ⋮ Rational homotopy via Sullivan models and enriched Lie algebras ⋮ Fixed points of \(n\)-valued maps on surfaces and the Wecken property -- a configuration space approach ⋮ Representation stability for homotopy groups of configuration spaces ⋮ Minimal generating and normally generating sets for the braid and mapping class groups of \(\mathbb D^2\), \(\mathbb S^2\) and \(\mathbb RP^2\). ⋮ Configuration space of geometric objects ⋮ The classification and the conjugacy classes of the finite subgroups of the sphere braid groups. ⋮ Wecken homotopies ⋮ Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane ⋮ The braid groups of the projective plane and the Fadell-Neuwirth short exact sequence. ⋮ The loop space homotopy type of simply-connected four-manifolds and their generalizations ⋮ The lower central and derived series of the braid groups of the projective plane. ⋮ Orbit configuration spaces associated to discrete subgroups of \(\mathrm{PSL}(2,\mathbb R)\) ⋮ THE BRAID GROUP $B_{n,m}(\mathbb{S}^{2})$ AND A GENERALISATION OF THE FADELL–NEUWIRTH SHORT EXACT SEQUENCE ⋮ On generalized configuration space and its homotopy groups ⋮ The lower central and derived series of the braid groups of the sphere ⋮ Bar complex, configuration spaces and finite type invariants for braids ⋮ Homotopy transfer and formality

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