Matching complexes, bounded degree graph complexes, and weight spaces of \(\mathrm{GL}_n\)-complexes

DOI10.1006/jabr.2000.8654zbMath0990.05144OpenAlexW2001690459MaRDI QIDQ5942786

Michelle L. Wachs, Victor Reiner, Karagueuzian, Dikran B.

Publication date: 28 April 2002

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

Full work available at URL: https://doi.org/10.1006/jabr.2000.8654

zbMATH Keywords

chessboard complexequivariant homology of graph and hypergraph complexesmatching complex

Mathematics Subject Classification ID

Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Equivariant homology and cohomology in algebraic topology (55N91) Combinatorial aspects of simplicial complexes (05E45) Homological methods in commutative ring theory (13D99)

Related Items (11)

Topology of bounded-degree graph complexes. ⋮ Representation stability for syzygies of line bundles on Segre-Veronese varieties ⋮ Generalized chessboard complexes and discrete Morse theory ⋮ An Explicit, Characteristic-Free, Equivariant Homology Equivalence Between Koszul Complexes ⋮ On the 3-torsion part of the homology of the chessboard complex ⋮ Multiple chessboard complexes and the colored Tverberg problem ⋮ Exact sequences for the homology of the matching complex ⋮ 𝑁₆ property for third Veronese embeddings ⋮ Symmetric multiple chessboard complexes and a new theorem of Tverberg type ⋮ Five-torsion in the homology of the matching complex on 14 vertices ⋮ Syzygies of the Veronese Modules

Cites Work

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• Homology of certain sets of 2-subgroups of symmetric groups
• The colored Tverberg's problem and complexes of injective functions
• On the Betti numbers of chessboard complexes
• Complexes of not \(i\)-connected graphs
• Shellability of chessboard complexes
• Minimal resolutions and the homology of matching and chessboard complexes
• Laplacian and homology of free two-step nilpotent Lie algebras
• Representation-theoretic interpretation of a formula of D. E. Littlewood
• Chessboard Complexes and Matching Complexes

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