Every finite simplicial complex is stably homotopy equivalent to a permutation complex, two-permutation complexes are wedges of spheres, and the complex of injective words Γ(K) admits an explicit wedge decomposition.
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On the topology of complexes of injective words
Every finite simplicial complex is stably homotopy equivalent to a permutation complex, two-permutation complexes are wedges of spheres, and the complex of injective words Γ(K) admits an explicit wedge decomposition.