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

Scott Balchin; Ethan MacBrough; Kyle Ormsby

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

Algebraic Topology 2024-06-14 v2 Combinatorics

Authors: Scott Balchin , Ethan MacBrough , Kyle Ormsby

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.

Keywords

n∞ operads transfer systems finite lattices dihedral groups cyclic groups homotopy combinatorics

Cite

@article{arxiv.2209.06992,
  title  = {The combinatorics of $N_\infty$ operads for $C_{qp^n}$ and $D_{p^n}$},
  author = {Scott Balchin and Ethan MacBrough and Kyle Ormsby},
  journal= {arXiv preprint arXiv:2209.06992},
  year   = {2024}
}

Comments

v2: pre-proofs version accepted in Glasgow Mathematical Journal, 21 pages, 2 figures. v1: 20 pages, 2 figures; comments welcome!

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

Abstract

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