Construction of $\mathbb{Z}_2$-harmonic 1-forms on closed 3-manifolds with long cylindrical necks
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912065270054912 |
|---|---|
| author | Salm, Willem Adriaan |
| author_facet | Salm, Willem Adriaan |
| contents | In this paper, we give an explicit construction of families of $\mathbb{Z}_2$-harmonic 1-forms that degenerate to manifolds with cylindrical ends. We do this by considering certain linear combinations of $L^2$-bounded $\mathbb{Z}_2$-harmonic 1-forms and by modifying the metric near the link. This construction can always be done if the homology group that counts $L^2$-bounded $\mathbb{Z}_2$-harmonic 1-forms is sufficiently large. This has the consequence that every smooth link can be obtained as the singular set of a $\mathbb{Z}_2$-harmonic 1-form on some 3-manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07015 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of $\mathbb{Z}_2$-harmonic 1-forms on closed 3-manifolds with long cylindrical necks Salm, Willem Adriaan Differential Geometry 53C99 In this paper, we give an explicit construction of families of $\mathbb{Z}_2$-harmonic 1-forms that degenerate to manifolds with cylindrical ends. We do this by considering certain linear combinations of $L^2$-bounded $\mathbb{Z}_2$-harmonic 1-forms and by modifying the metric near the link. This construction can always be done if the homology group that counts $L^2$-bounded $\mathbb{Z}_2$-harmonic 1-forms is sufficiently large. This has the consequence that every smooth link can be obtained as the singular set of a $\mathbb{Z}_2$-harmonic 1-form on some 3-manifold. |
| title | Construction of $\mathbb{Z}_2$-harmonic 1-forms on closed 3-manifolds with long cylindrical necks |
| topic | Differential Geometry 53C99 |
| url | https://arxiv.org/abs/2410.07015 |