Non‐loose Legendrian spheres with trivial contact homology DGA
Non‐loose Legendrian spheres with trivial contact homology DGA
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DOI：
10.1112/jtopol/jtw008
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发表时间：
2015-02
影响因子：
1.1
通讯作者：
T. Ekholm
中科院分区：
文献类型：
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作者：
T. Ekholm
Loose Legendrian n ‐子流形，n 2，由Murphy引入（'Loose Legendrian embeddings in high dimensional contact manifolds'，Preprint，2012，arXiv：1201.2245），并被证明在h‐原则意义上是灵活的：任何两个形式上是Legendrian isotope的loose Legendrian子流形实际上也是Legendrian isotope。勒让德接触同调是将微分分次代数（DGA）与勒让德子流形联系起来的Floer理论不变量。松散勒让德子流形的DGA是平凡的。我们通过在标准切触（2n+1）-空间n <$2中构造非松勒让德n-球面，证明了相反的结论是不正确的。
Loose Legendrian n ‐submanifolds, n⩾2 , were introduced by Murphy (‘Loose Legendrian embeddings in high dimensional contact manifolds’, Preprint, 2012, arXiv:1201.2245) and proved to be flexible in the h‐principle sense: any two loose Legendrian submanifolds that are formally Legendrian isotopic are also actually Legendrian isotopic. Legendrian contact homology is a Floer theoretic invariant that associates a differential graded algebra (DGA) to a Legendrian submanifold. The DGA of a loose Legendrian submanifold is trivial. We show that the converse is not true by constructing non‐loose Legendrian n ‐spheres in standard contact (2n+1) ‐space, n⩾2 , with trivial DGA.