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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.
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