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$N_\infty$-operads and associahedra

· 2019 · math.AT · arXiv 1905.03797

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abstract

We provide a new combinatorial approach to studying the collection of N-infinity-operads in G-equivariant homotopy theory for G a finite cyclic group. In particular, we show that for G the cyclic group of order p^n the natural order on the collection of N-infinity-operads stands in bijection with the poset structure of the (n+1)-associahedron. We further provide a lower bound for the number of possible N-infinity-operads for any finite cyclic group G.

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math.CT 1

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2025 1

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Eckmann-Hilton arguments in equivariant higher algebra

math.CT · 2025-08-07 · conditional · novelty 7.0

In equivariant higher algebra, the Boardman-Vogt tensor product of a k-connected and an l-connected G-operad is (k+l+2)-connected, given matching arity supports.

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  • Eckmann-Hilton arguments in equivariant higher algebra math.CT · 2025-08-07 · conditional · none · ref 1 · internal anchor

    In equivariant higher algebra, the Boardman-Vogt tensor product of a k-connected and an l-connected G-operad is (k+l+2)-connected, given matching arity supports.