A filtered generalization of the Chekanov-Eliashberg algebra
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866908449893253120 |
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| author | Avdek, Russell |
| author_facet | Avdek, Russell |
| contents | We define a new algebra associated to a Legendrian submanifold $Λ$ of a contact manifold of the form $\mathbb{R}_{t} \times W$, called the planar diagram algebra and denoted $PDA(Λ, \mathcal{P})$. It is a non-commutative, filtered, differential graded algebra whose filtered stable tame isomorphism class is an invariant of $Λ$ together with a partition $\mathcal{P}$ of its connected components. When $Λ$ is connected, $PDA$ is the Chekanov-Eliashberg algebra. In general, the $PDA$ differential counts holomorphic disks with multiple positive punctures using a combinatorial framework inspired by string topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_13031 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A filtered generalization of the Chekanov-Eliashberg algebra Avdek, Russell Symplectic Geometry Algebraic Topology Geometric Topology We define a new algebra associated to a Legendrian submanifold $Λ$ of a contact manifold of the form $\mathbb{R}_{t} \times W$, called the planar diagram algebra and denoted $PDA(Λ, \mathcal{P})$. It is a non-commutative, filtered, differential graded algebra whose filtered stable tame isomorphism class is an invariant of $Λ$ together with a partition $\mathcal{P}$ of its connected components. When $Λ$ is connected, $PDA$ is the Chekanov-Eliashberg algebra. In general, the $PDA$ differential counts holomorphic disks with multiple positive punctures using a combinatorial framework inspired by string topology. |
| title | A filtered generalization of the Chekanov-Eliashberg algebra |
| topic | Symplectic Geometry Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2205.13031 |