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arXiv · 2102.04415

Self-duality of the lattice of transfer systems via weak factorization systems

Evan E. Franchere·Kyle Ormsby·Angélica M Osorno·Weihang Qin·Riley Waugh
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Abstract

For a finite group $G$, $G$-transfer systems are combinatorial objects which encode the homotopy category of $G$-$N_\infty$ operads, whose algebras in $G$-spectra are $E_\infty$ $G$-spectra with a specified collection of multiplicative norms. For $G$ finite Abelian, we demonstrate a correspondence between $G$-transfer systems and weak factorization systems on the poset category of subgroups of $G$. This induces a self-duality on the lattice of $G$-transfer systems.

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Evan E. Franchere, Kyle Ormsby, Angélica M Osorno, Weihang Qin, Riley Waugh. 2021-02-08. Self-duality of the lattice of transfer systems via weak factorization systems. https://arxiv.org/abs/2102.04415

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