Contact surgery distance
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912770614624256 |
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| author | Kegel, Marc Nonino, Isacco Yadav, Monika |
| author_facet | Kegel, Marc Nonino, Isacco Yadav, Monika |
| contents | In this article, we define the contact surgery distance of two contact 3-manifolds $(M,ξ)$ and $(M',ξ')$ as the minimal number of contact surgeries needed to obtain $(M,ξ)$ from $(M',ξ')$. Our main result states that the contact surgery distance between two contact $3$-manifolds is at most $5$ larger than the topological surgery distance between the underlying smooth manifolds. As a byproduct of our proof, we classify the rational homology $3$-spheres on which the $d_3$-invariant of a $2$-plane field already determines its $Γ$-invariant and Euler class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14904 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Contact surgery distance Kegel, Marc Nonino, Isacco Yadav, Monika Geometric Topology 53D35, 53D10, 57K10, 57R65, 57K33 In this article, we define the contact surgery distance of two contact 3-manifolds $(M,ξ)$ and $(M',ξ')$ as the minimal number of contact surgeries needed to obtain $(M,ξ)$ from $(M',ξ')$. Our main result states that the contact surgery distance between two contact $3$-manifolds is at most $5$ larger than the topological surgery distance between the underlying smooth manifolds. As a byproduct of our proof, we classify the rational homology $3$-spheres on which the $d_3$-invariant of a $2$-plane field already determines its $Γ$-invariant and Euler class. |
| title | Contact surgery distance |
| topic | Geometric Topology 53D35, 53D10, 57K10, 57R65, 57K33 |
| url | https://arxiv.org/abs/2512.14904 |