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$N_\infty$-operads and associahedra

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arxiv 1905.03797 v3 pith:3SMTP223 submitted 2019-05-09 math.AT math.CO

Scott Balchin , David Barnes , Constanze Roitzheim This is my paper · ORCID
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keywords cyclicgroupn-infinity-operadscollectionfiniteorderapproachassociahedra
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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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  1. Eckmann-Hilton arguments in equivariant higher algebra

    math.CT 2025-08 conditional novelty 7.0 of 10

    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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