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Non-loose Legendrian spheres with trivial contact homology DGA
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. (Geometri)
2016 (English)In: Journal of Topology, ISSN 1753-8416, E-ISSN 1753-8424, Vol. 9, no 3, 826-848 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2016. Vol. 9, no 3, 826-848 p.
National Category
Geometry
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-287989DOI: 10.1112/jtopol/jtw008ISI: 000383709900006OAI: oai:DiVA.org:uu-287989DiVA: diva2:923684
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council, 2012-2365
Available from: 2016-04-27 Created: 2016-04-27 Last updated: 2016-11-03Bibliographically approved

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