Invariants of Knots, Embeddings and Immersions via Contact Geometry

Tobias Ekholm, John B. Etnyre

Published 2004-12-28Version 1

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.