We introduce two definitions of G-equivariant partitions of a finite G-set, both of which yield G-equivariant partition complexes. By considering suitable notions of equivariant trees, we show that G-equivariant partitions and G-trees are G-homotopy equivalent, generalizing existing results for the non-equivariant setting. Along the way, we develop equivariant versions of Quillen's Theorems A and B, which are of independent interest.
Keywords: partition complexes, trees, equivariant homotopy theory
2020 MSC: 55P91, 05A18, 20E08, 05E18
Theory and Applications of Categories, Vol. 45, 2026, No. 15, pp 501-536.
Published 2026-03-16.
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