Legendrian contact homology in |
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Authors: | Tobias Ekholm John Etnyre Michael Sullivan |
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Institution: | Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532 ; Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19105-6395 ; Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003-9305 |
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Abstract: | A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form , where 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 and, more generally, invariants of self transverse immersions into up to restricted regular homotopies. When , 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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Keywords: | |
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