Department of Mathematics FAS Harvard University One Oxford Street Cambridge MA 02138 USA Tel: (617) 495-2171 Fax: (617) 495-5132
To post a seminar which takes place at the Mathematics department, please email with date, time, room, title and possibly with an abstract.
TOPOLOGY SEMINAR: Michael Freedman
Microsoft and UCSB
Smooth embeddings of closed 3-manifolds in R^4
on Monday, September 15, 2014, at 10:20 AM - 12:00 PM in Science Center 232
I will present joint work with Ian Agol on smooth 3-manifolds in 4-space. It seems that only fairly primitive arguments obstruct the existence of such embeddings: For example no 3-manifold which embeds in a homology 4-sphere is known not to embed into S^4. I will give some new information on both existence of uniqueness of embeddings. The motivation for this study is that embeddings of 3 manifolds in R^4 impinges on the main open problems of low dimensional topology: The smooth Schoenflies conjecture, the smooth 4D Poincare conjecture, and the Andrews –Curtis conjecture.