Characterizing Transfer Systems for Non-Abelian Groups

Fuente: arXiv
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Main Authors: Klanderman, Sarah, Lewis, Chloe, Monson, Harlea, Shibata, Koki, Van Niel, Danika
Format: Preprint
Published: 2025
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author Klanderman, Sarah
Lewis, Chloe
Monson, Harlea
Shibata, Koki
Van Niel, Danika
author_facet Klanderman, Sarah
Lewis, Chloe
Monson, Harlea
Shibata, Koki
Van Niel, Danika
contents For a finite group $G$, the notion of a $G$-transfer system provides homotopy theorists with a combinatorial way to study equivariant objects. In this paper, we focus on the properties of transfer systems for non-abelian groups. We explicitly describe the width of all dihedral groups, quaternion groups, and dicyclic groups. For a given $G$, the set of all $G$-transfer systems forms a poset lattice under inclusion; these are a useful resource to homotopical combinatorialists for detecting patterns and checking conjectures. We expand the suite of known transfer system lattices for non-abelian groups including those which are dihedral, dicyclic, Frobenius, and alternating.
format Preprint
id arxiv_https___arxiv_org_abs_2511_13439
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Characterizing Transfer Systems for Non-Abelian Groups
Klanderman, Sarah
Lewis, Chloe
Monson, Harlea
Shibata, Koki
Van Niel, Danika
Algebraic Topology
Combinatorics
06B99, 55P91
For a finite group $G$, the notion of a $G$-transfer system provides homotopy theorists with a combinatorial way to study equivariant objects. In this paper, we focus on the properties of transfer systems for non-abelian groups. We explicitly describe the width of all dihedral groups, quaternion groups, and dicyclic groups. For a given $G$, the set of all $G$-transfer systems forms a poset lattice under inclusion; these are a useful resource to homotopical combinatorialists for detecting patterns and checking conjectures. We expand the suite of known transfer system lattices for non-abelian groups including those which are dihedral, dicyclic, Frobenius, and alternating.
title Characterizing Transfer Systems for Non-Abelian Groups
topic Algebraic Topology
Combinatorics
06B99, 55P91
url https://arxiv.org/abs/2511.13439