Grothendieck rigidity and virtual retraction of higher-rank GBS groups
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915793863704576 |
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| author | Wang, Daxun |
| author_facet | Wang, Daxun |
| contents | A rank $n$ generalized Baumslag-Solitar group ($GBS_n$ group) is a group that splits as a finite graph of groups such that all vertex and edge groups are isomorphic to $\mathbb{Z}^n$. This paper investigates Grothendieck rigidity and virtual retraction properties of $GBS_n$ groups. We show that every residually finite $GBS_n$ group is Grothendieck rigid. Further, we characterize when a $GBS_n$ group satisfies property (VRC), showing that it holds precisely when the monodromy is finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22477 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Grothendieck rigidity and virtual retraction of higher-rank GBS groups Wang, Daxun Group Theory 20E06, 20E18, 20E26 A rank $n$ generalized Baumslag-Solitar group ($GBS_n$ group) is a group that splits as a finite graph of groups such that all vertex and edge groups are isomorphic to $\mathbb{Z}^n$. This paper investigates Grothendieck rigidity and virtual retraction properties of $GBS_n$ groups. We show that every residually finite $GBS_n$ group is Grothendieck rigid. Further, we characterize when a $GBS_n$ group satisfies property (VRC), showing that it holds precisely when the monodromy is finite. |
| title | Grothendieck rigidity and virtual retraction of higher-rank GBS groups |
| topic | Group Theory 20E06, 20E18, 20E26 |
| url | https://arxiv.org/abs/2601.22477 |