Columbia Mathematics Department Colloquium


Invariants of embeddings and immersions via contact geometry


John Etnyre

Georgia Institute of Technology



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.


Wedensday, April 27th, 5:00 - 6:00 p.m.
Mathematics 520
Tea will be served at 4:30 p.m.