A note on Lagrangian cobordisms between Legendrian submanifolds of ℝ2n+1
A note on Lagrangian cobordisms between Legendrian submanifolds of ℝ2n+1
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关于ℝ2n+1 的勒格朗日子流形之间的拉格朗日配边的注记
DOI：
10.2140/pjm.2013.261.101
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发表时间：
2011
影响因子：
0.6
通讯作者：
R. Golovko
中科院分区：
文献类型：
--
作者：
R. Golovko
研究了两个闭的、可定向的legendrin子流形之间的内嵌拉格朗日协同关系。更确切地说，我们研究了在这种关系下Thurston-Bennequin数和（线性化的）Legendrian接触同调的行为。Thurston-Bennequin数的结果可以看作是Chantraine结果的推广，Chantraine结果在n = 1时成立。此外，我们给出了一些拉格朗日协边的构造，并证明了在1 （n+1）中存在无穷多对精确拉格朗日协边和非成对的Legendrian同位素Legendrian n-tori。©2013数学科学出版社。
We study the relation of an embedded Lagrangian cobordism between two closed, orientable Legendrian submanifolds of ℝ2n+1. More precisely, we investigate the behavior of the Thurston-Bennequin number and (linearized) Legendrian contact homology under this relation. The result about the Thurston-Bennequin number can be considered as a generalization of the result of Chantraine which holds when n = 1. In addition, we provide a few constructions of Lagrangian cobordisms and prove that there are infinitely many pairs of exact Lagrangian cobordant and not pairwise Legendrian isotopic Legendrian n-tori in ℝ2n+1. © 2013 Mathematical Sciences Publishers.