3/4/2010

Zhongtao Wu
Princeton University

Cosmetic Surgery Conjecture on S^3

It has been known over 40 years that every closed orientable 3-manifold is obtained by surgery on a link in S3. However, a complete classification has remained elusive due to the lack of uniqueness of this surgery description. In this talk, we discuss the following uniqueness theorem for Dehn surgey on a nontrivial knot in S3. Let K be a knot in S3, and let r and r' be two distinct rational numbers of same sign, allowing r to be infinite; then there is no orientation preserving homeomophism between the manifolds obtained by performing Dehn surgery of type r and r', respectively. In particular, this result implies the Knot Complement Theorem of Gordon and Luecke.