Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.02730 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In this paper we provide two new constructions that are useful for the theory of projection complexes developed by Bestvina, Bromberg, Fujiwara and Sisto. We prove that there exists a subtree of the projection complex which is quasiisometric to the projection complex. We use this subtree to form a tree of metric spaces, which is a subgraph of the quasi-tree of metrics spaces and quasiisometric to it. These constructions simplify the metric structure (up to quasiisometry) of the projection complex and the quasi-tree of metric spaces. As an application, we use these constructions to provide a shorter proof of Hume's theorem that the mapping class group admits a quasiisometric embedding into a finite product of trees.