An L ∞ $L_\infty$ structure for Legendrian contact homology

IF 1.1 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2025-07-31 DOI:10.1112/topo.70034

Lenhard Ng

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引用次数: 0

Abstract

For any Legendrian knot or link in $R^{3}$ , we construct an $L_{\infty}$ algebra that can be viewed as an extension of the Chekanov–Eliashberg differential graded algebra. The $L_{\infty}$ structure incorporates information from rational symplectic field theory and can be formulated combinatorially. One consequence is the construction of a Poisson bracket on commutative Legendrian contact homology, and we show that the resulting Poisson algebra is an invariant of Legendrian links under isotopy.

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Legendrian接触同调的L∞$L_\infty$结构

对于r3中的任意Legendrian结或连杆$\mathbb {R}^3$，我们构造了一个L∞$L_\infty$代数，它可以看作是Chekanov-Eliashberg微分梯度代数的扩展。L∞$L_\infty$结构包含了来自理性辛场论的信息，并且可以组合地表述。一个结果是在交换Legendrian接触同调上构造了一个泊松括号，并证明了所得到的泊松代数是同位素下Legendrian连杆的不变量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.