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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Legendrian contact homology in $ P \times \mathbb{R}$


Authors: Tobias Ekholm, John Etnyre and Michael Sullivan
Journal: Trans. Amer. Math. Soc. 359 (2007), 3301-3335
MSC (2000): Primary 53D10
Published electronically: January 26, 2007
MathSciNet review: 2299457
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Abstract: A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form $ P\times \mathbb{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 $ \mathbb{R}^n$ and, more generally, invariants of self transverse immersions into $ \mathbb{R}^n$ 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.


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Additional Information

Tobias Ekholm
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
Address at time of publication: Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden

John Etnyre
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19105-6395
Address at time of publication: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160

Michael Sullivan
Affiliation: Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003-9305

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04337-1
PII: S 0002-9947(07)04337-1
Received by editor(s): June 3, 2005
Published electronically: January 26, 2007
Additional Notes: The first author was partially supported by the Alfred P. Sloan Foundation, NSF grant DMS-0505076, and a research fellowship of the Royal Swedish Academy of Science sponsored by the Knut and Alice Wallenberg foundation.
The second author was partially supported by the NSF CAREER grant DMS-0239600 and NSF Focused Research grant FRG-0244663.
The third author was partially supported by NSF grant DMS-0305825 and MSRI
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.