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arXiv · 2209.06992

The combinatorics of $N_\infty$ operads for $C_{qp^n}$ and $D_{p^n}$

Scott Balchin·Ethan MacBrough·Kyle Ormsby
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Abstract

We provide a general recursive method for constructing transfer systems on finite lattices. Using this we calculate the number of homotopically distinct $N_\infty$ operads for dihedral groups $D_{p^n}$, $p > 2$ prime, and cyclic groups $C_{qp^n}$, $p \neq q$ prime. We then further display some of the beautiful combinatorics obtained by restricting to certain homotopically meaningful $N_\infty$ operads for these groups.

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Scott Balchin, Ethan MacBrough, Kyle Ormsby. 2022-09-15. The combinatorics of $N_\infty$ operads for $C_{qp^n}$ and $D_{p^n}$. https://arxiv.org/abs/2209.06992

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