Parametric satellites and connected-sums in the space of Legendrian embeddings
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913368988712960 |
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| author | Fernández, Eduardo Martínez-Aguinaga, Javier Presas, Francisco |
| author_facet | Fernández, Eduardo Martínez-Aguinaga, Javier Presas, Francisco |
| contents | This article introduces two new constructions at the higher homotopy level in the space of Legendrian embeddings in $(\mathbb{R}^3, ξ_{\operatorname{std}})$. We first introduce the parametric Legendrian satellite construction, showing that the satellite operation works for parametric families of Legendrian embeddings. This yields new invariants at the higher-order homotopy level.
We then introduce the parametric connected-sum construction. This operation takes as inputs two $n$-spheres based at Legendrian embeddings $K_1$ and $K_2$, respectively, and produces a new $n$-sphere based at $K_1\# K_2$. As a main application we construct new infinite families of loops of Legendrian embeddings with non-trivial LCH monodromy invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parametric satellites and connected-sums in the space of Legendrian embeddings Fernández, Eduardo Martínez-Aguinaga, Javier Presas, Francisco Symplectic Geometry Differential Geometry Geometric Topology 53D10 This article introduces two new constructions at the higher homotopy level in the space of Legendrian embeddings in $(\mathbb{R}^3, ξ_{\operatorname{std}})$. We first introduce the parametric Legendrian satellite construction, showing that the satellite operation works for parametric families of Legendrian embeddings. This yields new invariants at the higher-order homotopy level. We then introduce the parametric connected-sum construction. This operation takes as inputs two $n$-spheres based at Legendrian embeddings $K_1$ and $K_2$, respectively, and produces a new $n$-sphere based at $K_1\# K_2$. As a main application we construct new infinite families of loops of Legendrian embeddings with non-trivial LCH monodromy invariant. |
| title | Parametric satellites and connected-sums in the space of Legendrian embeddings |
| topic | Symplectic Geometry Differential Geometry Geometric Topology 53D10 |
| url | https://arxiv.org/abs/2405.19280 |