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Legendrian contact homology in P x R
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. (Matematik 1-5)
2007 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 359, no 7, 3301-3335 p.Article in journal (Refereed) Published
Abstract [en]

A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form P × ℝ, where P is an exact symplectic manifold, is established. The class of such contact manifolds includes 1-jet spaces of smooth manifolds. As an application, contact homology is used to provide (smooth) isotopy invariants of submanifolds of ℝn and, more generally, invariants of self transverse immersions into ℝn up to restricted regular homotopies. When n = 3, this application is the first step in extending and providing a contact geometric underpinning for the new knot invariants of Ng.

Place, publisher, year, edition, pages
2007. Vol. 359, no 7, 3301-3335 p.
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Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-12640DOI: 10.1090/S0002-9947-07-04337-1ISI: 000245149100015OAI: oai:DiVA.org:uu-12640DiVA: diva2:40409
Available from: 2008-01-08 Created: 2008-01-08 Last updated: 2017-12-11Bibliographically approved

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Ekholm, Tobias

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