Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold
Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold
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亚临界韦恩斯坦 4 流形边界中的勒让德接触同调
DOI：
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发表时间：
2013
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通讯作者：
Lenhard L. Ng
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作者：
T. Ekholm;Lenhard L. Ng
我们给出了与 $S^1 imes S^2$ 或任何连通和 $#^k(S^1 imes S^2)$ 中的 Legendrian 链接相关联的 Legendrian 接触同调代数的组合描述，将其视为通过将 1-handle 附加到 4-ball 获得的 Weinstein 流形的接触边界。鉴于辛同调的手术公式，这给出了任何 4 维韦恩斯坦流形（及其边界的线性化接触同调）的辛同调的组合描述。我们还从组合和分析的角度研究了例子并讨论了变形下传奇同调代数的不变性。
We give a combinatorial description of the Legendrian contact homology algebra associated to a Legendrian link in $S^1 imes S^2$ or any connected sum $#^k(S^1 imes S^2)$, viewed as the contact boundary of the Weinstein manifold obtained by attaching 1-handles to the 4-ball. In view of the surgery formula for symplectic homology, this gives a combinatorial description of the symplectic homology of any 4-dimensional Weinstein manifold (and of the linearized contact homology of its boundary). We also study examples and discuss the invariance of the Legendrian homology algebra under deformations, from both the combinatorial and the analytical perspectives.