The fundamental group of the Quillen complex of the symmetric group

DOI10.1016/j.jalgebra.2004.07.025zbMath1060.55002OpenAlexW2002186754MaRDI QIDQ1888802

Rached Ksontini

Publication date: 29 November 2004

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.07.025

zbMATH Keywords

posetfundamental groupsymmetric groupQuillen complexsubgroup complex

Mathematics Subject Classification ID

Series and lattices of subgroups (20D30) Classification of homotopy type (55P15) Topological methods in group theory (57M07) Fundamental group, presentations, free differential calculus (57M05) Simplicial sets and complexes in algebraic topology (55U10) Subgroups of symmetric groups (20B35)

Related Items (9)

Endotrivial modules for finite groups via homotopy theory ⋮ On the homotopy type of complexes of graphs with bounded domination number ⋮ Simple connectivity of the Quillen complex of the symmetric group. ⋮ The homotopy types of the posets of \(p\)-subgroups of a finite group ⋮ SYMMETRY GEOMETRY BY PAIRINGS ⋮ A stronger reformulation of Webb's conjecture in terms of finite topological spaces ⋮ Pairings and related symmetry notions ⋮ The fundamental group of the p‐subgroup complex ⋮ Top homology of hypergraph matching complexes, \(p\)-cycle complexes and Quillen complexes of symmetric groups.

Cites Work

• Simple connectivity of \(p\)-group complexes
• Homotopy equivalence of posets with a group action
• Homology of certain sets of 2-subgroups of symmetric groups
• Homotopy properties of the poset of nontrivial p-subgroups of a group
• Simple connectivity of the Quillen complex of the symmetric group.
• Stable homotopy
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