Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.21806 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916903962804224 |
|---|---|
| author | Boyd, Rachael Bregman, Corey |
| author_facet | Boyd, Rachael Bregman, Corey |
| contents | We study the unparametrised smooth embedding space of a Hopf link in $\mathbb{R}^3$, and prove that it is homotopy equivalent to the closed 3-manifold $S^3/\mathbb{Q}_8$. As an intermediate step in the proof, we show that the inclusion of the subspace of round embeddings is a homotopy equivalence. We provide analogous results for the unparametrised smooth embedding space of a Hopf link in $S^3$, which we show is homotopy equivalent to $\mathbb{R} P^2\times \mathbb{R} P^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21806 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The embedding space of a Hopf link Boyd, Rachael Bregman, Corey Geometric Topology 58D10, 55P15 We study the unparametrised smooth embedding space of a Hopf link in $\mathbb{R}^3$, and prove that it is homotopy equivalent to the closed 3-manifold $S^3/\mathbb{Q}_8$. As an intermediate step in the proof, we show that the inclusion of the subspace of round embeddings is a homotopy equivalence. We provide analogous results for the unparametrised smooth embedding space of a Hopf link in $S^3$, which we show is homotopy equivalent to $\mathbb{R} P^2\times \mathbb{R} P^2$. |
| title | The embedding space of a Hopf link |
| topic | Geometric Topology 58D10, 55P15 |
| url | https://arxiv.org/abs/2504.21806 |