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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.07853 |
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| _version_ | 1866915993661472768 |
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| author | Leary, Ian J. Petrosyan, Nansen |
| author_facet | Leary, Ian J. Petrosyan, Nansen |
| contents | Let $G_Γ$ be a graph product over a finite simplicial graph $Γ$, and let $K_Γ$ denote the kernel of the canonical homomorphism from $G_Γ$ to the direct product of its vertex groups. It is known that, up to isomorphism, $K_Γ$ depends only on the underlying graph $Γ$ and the cardinalities of the vertex groups.
In this paper we establish a functorial refinement of this fact. We show that any collection of set maps between the vertex groups naturally induces a homomorphism between the corresponding kernels, and that this construction is functorial. Several applications are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07853 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal Structure of Graph Product Kernels Leary, Ian J. Petrosyan, Nansen Group Theory Algebraic Topology Let $G_Γ$ be a graph product over a finite simplicial graph $Γ$, and let $K_Γ$ denote the kernel of the canonical homomorphism from $G_Γ$ to the direct product of its vertex groups. It is known that, up to isomorphism, $K_Γ$ depends only on the underlying graph $Γ$ and the cardinalities of the vertex groups. In this paper we establish a functorial refinement of this fact. We show that any collection of set maps between the vertex groups naturally induces a homomorphism between the corresponding kernels, and that this construction is functorial. Several applications are discussed. |
| title | Universal Structure of Graph Product Kernels |
| topic | Group Theory Algebraic Topology |
| url | https://arxiv.org/abs/2605.07853 |