Iterated power set applications generate a hierarchy of operads linking the permutative operad to triassociative, substitution, and composition operads, plus a new operad on relative simplicial complexes governed by join polyhedral products.
arXiv:2306.05230 [math]
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Describes the quasi-Lie subalgebra QL(K) and Pi-subalgebra S(K) in the homotopy groups of DJ(K) and proves S(K) equals the full homotopy groups precisely when K is a flag complex.
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Power set operads
Iterated power set applications generate a hierarchy of operads linking the permutative operad to triassociative, substitution, and composition operads, plus a new operad on relative simplicial complexes governed by join polyhedral products.
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Iterated Whitehead products in the homotopy groups of polyhedral products
Describes the quasi-Lie subalgebra QL(K) and Pi-subalgebra S(K) in the homotopy groups of DJ(K) and proves S(K) equals the full homotopy groups precisely when K is a flag complex.