Abstract:
One of the most basic questions in topology is how one
manifold can sit inside of another; the classical study of knots in
3space is a special case of this. After recalling some classical
results about embeddings of manifolds I will discuss the conormal
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.
