Characterizing Transfer Systems for Non-Abelian Groups
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908988571910144 |
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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 |
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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 |