Homology, Homotopy and Applications

Volume 24 (2022)

Number 2

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

Pages: 115 – 134

DOI: https://dx.doi.org/10.4310/HHA.2022.v24.n2.a6

Authors

Evan E. Franchere (Department of Mathematics, Reed College, Portland, Oregon, U.S.A.)

Kyle Ormsby (Department of Mathematics, Reed College, Portland, Oregon, U.S.A.)

Angélica M. Osorno (Department of Mathematics, Reed College, Portland, Oregon, U.S.A.)

Weihang Qin (Department of Mathematics, Reed College, Portland, Oregon, U.S.A.)

Riley Waugh (Department of Mathematics, Reed College, Portland, Oregon, U.S.A.)

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.

Keywords

transfer system, weak factorization system

2010 Mathematics Subject Classification

18A32, 55P91

Received 16 February 2021

Received revised 10 June 2021

Published 10 August 2022