Invariants of Knots, Embeddings and Immersions via Contact Geometry
Joint work with Tobias Ekholm.
Fields Inst. Commun. 47 (2005), 77--96.

This paper is an overview of the idea of using contact geometry to construct invariants of immersions and embeddings. In particular, it discusses how to associate a contact manifold to any manifold and a Legendrian submanifold to an embedding or immersion. We then discuss recent work that creates invariants of immersions and embeddings using the Legendrian contact homology of the associated Legendrian submanifold.

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