Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.12162 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913320472150016 |
|---|---|
| author | Zbinden, Stefanie |
| author_facet | Zbinden, Stefanie |
| contents | Given a geodesic metric space $X$, we construct a corresponding hyperbolic space, which we call the contraction space, that detects all strongly contracting directions in the following sense; a geodesic in $X$ is strongly contracting if and only if its parametrized image in the contraction space is a quasi-geodesic. If a finitely generated group $G$ acts geometrically on $X$, then all strongly-contracting elements act as WPD elements on the contraction space. If the space $X$ is CAT(0), or more generally Morse-dichotomous, that is if all Morse geodesics are strongly-contracting, then all generalized loxodromics act as WPD elements, implying that the action is what we call ``universally WPD''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12162 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperbolic spaces that detect all strongly-contracting directions Zbinden, Stefanie Group Theory Metric Geometry 20F65 Given a geodesic metric space $X$, we construct a corresponding hyperbolic space, which we call the contraction space, that detects all strongly contracting directions in the following sense; a geodesic in $X$ is strongly contracting if and only if its parametrized image in the contraction space is a quasi-geodesic. If a finitely generated group $G$ acts geometrically on $X$, then all strongly-contracting elements act as WPD elements on the contraction space. If the space $X$ is CAT(0), or more generally Morse-dichotomous, that is if all Morse geodesics are strongly-contracting, then all generalized loxodromics act as WPD elements, implying that the action is what we call ``universally WPD''. |
| title | Hyperbolic spaces that detect all strongly-contracting directions |
| topic | Group Theory Metric Geometry 20F65 |
| url | https://arxiv.org/abs/2404.12162 |