Knots, links, and 4-manifolds
Ronald J. Stern
(University of California, Irvine)
Saturday, November 9, 1996
2:30 PM
Is there a reasonable conjectured smooth classification of
simply-connected closed smooth 4-manifolds? The goal of this talk is to
support the folk conjecture that any reasonable conjecture is false. The
most recent such conjecture was that any irreducible simply-connected
smooth 4-manifold is symplectic, i.e. has a non-degenerate closed
2-form. In this talk we show that this is wildly false by discussing
the recently discovered relationship (joint work with Ron Fintushel)
between isotopy classes of knots and links in S3 and
the diffeomorphism types of homeomorphic smooth 4-manifolds. Along the
way we will survey all the recent developments in understanding smooth
4-manifolds.
Back to
Fall 1996 meeting of the PNGS.
Suggestions or corrections to
Jack Lee <lee@math.washington.edu>.