Top homology of hypergraph matching complexes, \(p\)-cycle complexes and Quillen complexes of symmetric groups.

DOI10.1016/j.jalgebra.2008.11.042zbMath1188.20060arXiv0808.3114OpenAlexW2013176841MaRDI QIDQ1048941

Michelle L. Wachs, John Shareshian

Publication date: 8 January 2010

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

Full work available at URL: https://arxiv.org/abs/0808.3114

zbMATH Keywords

representations of symmetric groupshomology groupsQuillen complexeshypergraph matching complexes

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Series and lattices of subgroups (20D30) Classification of homotopy type (55P15) Homological methods in group theory (20J05) Simplicial sets and complexes in algebraic topology (55U10) Combinatorial aspects of simplicial complexes (05E45)

Related Items (4)

Endotrivial modules for finite groups via homotopy theory ⋮ Matching and independence complexes related to small grids ⋮ On a conjecture of Stein ⋮ Poset fiber theorems

Cites Work

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• Decompositions and connectivity of matching and chessboard complexes
• Torsion in the matching complex and chessboard complex
• Exact sequences for the homology of the matching complex
• Five-torsion in the homology of the matching complex on 14 vertices
• Exponentiation and Steinberg modules
• 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
• Simple connectivity of the Quillen complex of the symmetric group.
• On Quillen's conjecture for the \(p\)-groups complex
• Hypergraph matching complexes and Quillen complexes of symmetric groups.
• The fundamental group of the Quillen complex of the symmetric group
• Topology of matching, chessboard, and general bounded degree graph complexes
• Poset fiber theorems
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• Combinatorial Laplacian of the matching complex

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