Hypergraph matching complexes and Quillen complexes of symmetric groups.

DOI10.1016/j.jcta.2004.03.002zbMath1059.20019OpenAlexW1997826592MaRDI QIDQ1826947

John Shareshian

Publication date: 6 August 2004

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2004.03.002

zbMATH Keywords

symmetric groupssimplicial complexesQuillen complexeshypergraph matching complexesposets of partitions

Mathematics Subject Classification ID

Series and lattices of subgroups (20D30) Classification of homotopy type (55P15) Homological methods in group theory (20J05) Topological lattices (06B30) Homology and cohomology theories in algebraic topology (55N99) Symmetric groups (20B30)

Related Items (7)

Endotrivial modules for finite groups via homotopy theory ⋮ Elementary Abelian subgroups in \(p\)-groups with a cyclic derived subgroup. ⋮ On the homotopy type of the Quillen complex of finite soluble groups ⋮ Conjugate $p$-elements of full support that generate the wreath product $C_{p}wr C_{p}$ ⋮ The clique operator on matching and chessboard graphs ⋮ 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

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• Simple connectivity of \(p\)-group complexes
• Decompositions and connectivity of matching and chessboard complexes
• Homology of certain sets of 2-subgroups of symmetric groups
• Euler characteristics of discrete groups and G-spaces
• Euler characteristics of groups: The \(p\)-fractional part
• Homotopy properties of the poset of nontrivial p-subgroups of a group
• Some results about Quillen complex of \(\text{Sp}_{2n}(q)\)
• Simple connectivity of the Quillen complex of the symmetric group.
• Topology of subgroup lattices of symmetric and alternating groups.
• The homology of ``\(k\)-equal manifolds and related partition lattices
• The Quillen complex of groups of symplectic type: the characteristic 2 case.
• Topology of matching, chessboard, and general bounded degree graph complexes
• Chessboard Complexes and Matching Complexes

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