Columbia Mathematics Department Colloquium
Invariants of embeddings and immersions via contact geometry
by
John Etnyre
Georgia Institute of Technology
Abstract:
One of the most basic questions in topology is how one manifold can sit inside of another; the classical study of knots in 3-space is a special case of this. After recalling some classical results about embeddings of manifolds I will discuss the co-normal construction. This construction introduces geometry, specifically contact geometry, into this purely topological problem. While this construction has been around for quite some time --- for example, Arnold used it to study ``wave fronts" --- new tools in contact geometry, namely Legendrian contact homology, have allowed one to see more subtle information about embeddings. I will describe these tools and some of the recent results one can prove with them.