A Combination Theorem for Trees of Metric Bundles
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908548243390464 |
|---|---|
| author | Halder, Rakesh |
| author_facet | Halder, Rakesh |
| contents | Motivated by the work of Bestvina-Feighn ([BF92]) and Mj-Sardar ([MS12]), we define trees of metric bundles subsuming both the trees of metric spaces and the metric bundles. Then we prove a combination theorem for these spaces. More precisely, we prove that the total space of a tree of metric bundles is hyperbolic if the following hold (see Theorem $1.5$). $(1)$ The fibers are uniformly hyperbolic metric spaces and the base is also hyperbolic metric space, $(2)$ barycenter maps for the fibers are uniformly coarsely surjective, $(3)$ the edge spaces are uniformly qi embedded in the corresponding fibers and $(4)$ the Bestvina-Feighn hallway flaring condition is satisfied.
As an application, we provide a combination theorem for certain complexes of groups over finite simplicial complex (see Theorem $1.3$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_14692 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Combination Theorem for Trees of Metric Bundles Halder, Rakesh Metric Geometry 20F65, 20F67 (primary), 57M07 (secondary) Motivated by the work of Bestvina-Feighn ([BF92]) and Mj-Sardar ([MS12]), we define trees of metric bundles subsuming both the trees of metric spaces and the metric bundles. Then we prove a combination theorem for these spaces. More precisely, we prove that the total space of a tree of metric bundles is hyperbolic if the following hold (see Theorem $1.5$). $(1)$ The fibers are uniformly hyperbolic metric spaces and the base is also hyperbolic metric space, $(2)$ barycenter maps for the fibers are uniformly coarsely surjective, $(3)$ the edge spaces are uniformly qi embedded in the corresponding fibers and $(4)$ the Bestvina-Feighn hallway flaring condition is satisfied. As an application, we provide a combination theorem for certain complexes of groups over finite simplicial complex (see Theorem $1.3$). |
| title | A Combination Theorem for Trees of Metric Bundles |
| topic | Metric Geometry 20F65, 20F67 (primary), 57M07 (secondary) |
| url | https://arxiv.org/abs/2206.14692 |