A bordered Chekanov–Eliashberg algebra
A bordered Chekanov–Eliashberg algebra
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有界 Chekanov-Eliashberg 代数
DOI：
10.1112/jtopol/jtq035
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发表时间：
2010
影响因子：
1.1
通讯作者：
Steven Sivek
中科院分区：
文献类型：
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作者：
Steven Sivek
给定 ℝ3 中勒让德结 K 的前投影，该结沿垂直线被切成几块，我们为每块分配一个微分分级代数，并证明将 K 的 Chekanov-Eliashberg 不变量描述为这些代数的推出的 van Kampen 定理。然后，我们使用该定理构建由某些缠结替换相关的勒让德结不变量之间的映射，并描述勒让德怀特海双打的线性化接触同源性。其他推论包括用于线性化接触同调的 Mayer-Vietoris 序列和用于 Legendrian 结特征代数的 van Kampen 定理。
Given a front projection of a Legendrian knot K in ℝ3, which has been cut into several pieces along vertical lines, we assign a differential graded algebra to each piece and prove a van Kampen theorem describing the Chekanov–Eliashberg invariant of K as a pushout of these algebras. We then use this theorem to construct maps between the invariants of Legendrian knots related by certain tangle replacements, and to describe the linearized contact homology of Legendrian Whitehead doubles. Other consequences include a Mayer–Vietoris sequence for linearized contact homology and a van Kampen theorem for the characteristic algebra of a Legendrian knot.