Non-loose Legendrian spheres with trivial contact homology DGA

作者：Ekholm Tobias^*

来源：Journal of Topology, 2016, 9(3): 826-848.

DOI：10.1112/jtopol/jtw008

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.

• 出版日期2016-9