Taut foliations, left-orders, and pseudo-Anosov mapping tori
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913629677289472 |
|---|---|
| author | Zung, Jonathan |
| author_facet | Zung, Jonathan |
| contents | For a large class of 3-manifolds with taut foliations, we construct an action of $π_1(M)$ on $\mathbb{R}$ by orientation preserving homeomorphisms which captures the transverse geometry of the leaves. This action is complementary to Thurston's universal circle. Applications include the left-orderability of the fundamental groups of every non-trivial surgery on the figure eight knot. Our techniques also apply to at least 2598 manifolds representing 44.7% of the non-L-space rational homology spheres in the Hodgson-Weeks census of small closed hyperbolic 3-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_07706 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Taut foliations, left-orders, and pseudo-Anosov mapping tori Zung, Jonathan Geometric Topology 57R30 For a large class of 3-manifolds with taut foliations, we construct an action of $π_1(M)$ on $\mathbb{R}$ by orientation preserving homeomorphisms which captures the transverse geometry of the leaves. This action is complementary to Thurston's universal circle. Applications include the left-orderability of the fundamental groups of every non-trivial surgery on the figure eight knot. Our techniques also apply to at least 2598 manifolds representing 44.7% of the non-L-space rational homology spheres in the Hodgson-Weeks census of small closed hyperbolic 3-manifolds. |
| title | Taut foliations, left-orders, and pseudo-Anosov mapping tori |
| topic | Geometric Topology 57R30 |
| url | https://arxiv.org/abs/2006.07706 |