Fundamental Groups of Disjointly Tree-Graded Spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917321783640064 |
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| author | Brazas, Jeremy Kent, Curtis |
| author_facet | Brazas, Jeremy Kent, Curtis |
| contents | Tree-graded spaces are a generalization of $\mathbb{R}$-trees and play an important role in describing the large-scale geometry of relatively hyperbolic groups. We consider a subclass of tree-graded spaces that we call "disjointly tree-graded spaces," determined by maps to $\mathbb{R}$-trees. We characterize the fundamental group of a disjointly tree-graded space $(X,\mathscr{P})$ in terms of the fundamental groups of its pieces. Our results apply even in cases where neither $X$ nor its pieces are locally simply connected. In particular, we show that if the pieces are uniformly $1$-$UV_0$, then the fundamental group of a disjointly tree-graded space embeds into the inverse limit of the free products of the fundamental groups of finitely many pieces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07282 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fundamental Groups of Disjointly Tree-Graded Spaces Brazas, Jeremy Kent, Curtis Algebraic Topology Group Theory Geometric Topology 55Q52, 20F34, 57M10, 20F69, 55P55 Tree-graded spaces are a generalization of $\mathbb{R}$-trees and play an important role in describing the large-scale geometry of relatively hyperbolic groups. We consider a subclass of tree-graded spaces that we call "disjointly tree-graded spaces," determined by maps to $\mathbb{R}$-trees. We characterize the fundamental group of a disjointly tree-graded space $(X,\mathscr{P})$ in terms of the fundamental groups of its pieces. Our results apply even in cases where neither $X$ nor its pieces are locally simply connected. In particular, we show that if the pieces are uniformly $1$-$UV_0$, then the fundamental group of a disjointly tree-graded space embeds into the inverse limit of the free products of the fundamental groups of finitely many pieces. |
| title | Fundamental Groups of Disjointly Tree-Graded Spaces |
| topic | Algebraic Topology Group Theory Geometric Topology 55Q52, 20F34, 57M10, 20F69, 55P55 |
| url | https://arxiv.org/abs/2603.07282 |