Pseudo-Legendrian and Legendrian Simplicity of Links in 3-Manifolds
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| Format: | Preprint |
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2025
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| _version_ | 1866911383668391936 |
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| author | Cahn, Patricia Chatterjee, Rima Chernov, Vladimir |
| author_facet | Cahn, Patricia Chatterjee, Rima Chernov, Vladimir |
| contents | We construct infinite families of non-simple isotopy classes of links in overtwisted contact structures on $S^1$-bundles over surfaces. These examples include: (1) a pair of Legendrian links that are not Legendrian isotopic, but which are isotopic as framed links, homotopic as Legendrian immersed multi-curves, and have Legendrian-isotopic components and (2) a pair of Legendrian links that are not Legendrian isotopic, but are isotopic as framed links, homotopic as Legendrian immersed multi-curves, and which are link-homotopic as Legendrian links. Moreover, we construct examples showing that both of these non-simplicity phenomena can occur in the same smooth isotopy class. To construct these examples, we develop the theory of links transverse to a nowhere-zero vector field in a 3-manifold, and construct analogous examples in the category of links transverse to a vector field. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_18185 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pseudo-Legendrian and Legendrian Simplicity of Links in 3-Manifolds Cahn, Patricia Chatterjee, Rima Chernov, Vladimir Geometric Topology Symplectic Geometry 57K10, 57K33 We construct infinite families of non-simple isotopy classes of links in overtwisted contact structures on $S^1$-bundles over surfaces. These examples include: (1) a pair of Legendrian links that are not Legendrian isotopic, but which are isotopic as framed links, homotopic as Legendrian immersed multi-curves, and have Legendrian-isotopic components and (2) a pair of Legendrian links that are not Legendrian isotopic, but are isotopic as framed links, homotopic as Legendrian immersed multi-curves, and which are link-homotopic as Legendrian links. Moreover, we construct examples showing that both of these non-simplicity phenomena can occur in the same smooth isotopy class. To construct these examples, we develop the theory of links transverse to a nowhere-zero vector field in a 3-manifold, and construct analogous examples in the category of links transverse to a vector field. |
| title | Pseudo-Legendrian and Legendrian Simplicity of Links in 3-Manifolds |
| topic | Geometric Topology Symplectic Geometry 57K10, 57K33 |
| url | https://arxiv.org/abs/2512.18185 |