Embedding theory for contractible manifolds - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T09:40:54Z http://mathoverflow.net/feeds/question/42106 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/42106/embedding-theory-for-contractible-manifolds Embedding theory for contractible manifolds Victor 2010-10-14T03:35:14Z 2010-10-14T07:15:20Z <p>What is known about spaces of embeddings of contractible manifolds into Euclidean space? I am also curious about the case of small codimension (or even codimension 0). The same question about the configuration spaces in such manifolds. </p> http://mathoverflow.net/questions/42106/embedding-theory-for-contractible-manifolds/42125#42125 Answer by Bruno Martelli for Embedding theory for contractible manifolds Bruno Martelli 2010-10-14T07:15:20Z 2010-10-14T07:15:20Z <p>(This is by far not a complete answer, just an example.) In dimension 4, a <a href="http://nyjm.albany.edu:8000/PacJ/p/2003/209-2-8.pdf" rel="nofollow">paper of Livingstone</a> (build on previous work of Lickorish) constructs some (compact with boundary) contractible 4-manifold which embeds in \$\mathbb R^4\$ in infinitely many (countable) distinct ways. These are distinguished by the fundamental group of the complement. </p>