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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Legendrian contact homology in $P \times \mathbb {R}$
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by Tobias Ekholm, John Etnyre and Michael Sullivan PDF
Trans. Amer. Math. Soc. 359 (2007), 3301-3335 Request permission

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
  • MR Author ID: 641675
  • 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
  • MR Author ID: 619395
  • Michael Sullivan
  • Affiliation: Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003-9305
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 3301-3335
  • MSC (2000): Primary 53D10
  • DOI: https://doi.org/10.1090/S0002-9947-07-04337-1
  • MathSciNet review: 2299457