Cycle-free chessboard complexes and symmetric homology of algebras. (English) Zbl 1207.05228
Summary: Chessboard complexes and their relatives have been an important recurring theme of topological combinatorics. Closely related “cycle-free chessboard complexes” have been recently introduced by Ault and Fiedorowicz in [S. Ault and Z. Fiedorowicz, “Symmetric homology of algebras, ” arXiv:0708.1575v54 [math.AT] 5 Nov 2007; Z. Fiedorowicz, “Question about a simplicial complex,” Algebraic Topology Discussion List (maintained by Don Davis) http://www.lehigh.edu/~dmd1/zf93] as a tool for computing symmetric analogues of the cyclic homology of algebras. We study connectivity properties of these complexes and prove a result that confirms a strengthened conjecture from [S. Ault and {|it Z. Fiedorowicz}, loc. cit.].
MSC:
| 05E45 | Combinatorial aspects of simplicial complexes |
| 05C20 | Directed graphs (digraphs), tournaments |
| 05E15 | Combinatorial aspects of groups and algebras (MSC2010) |
| 16E40 | (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) |
| 19D55 | \(K\)-theory and homology; cyclic homology and cohomology |
| 55U10 | Simplicial sets and complexes in algebraic topology |
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