| Résume | Daniel Ruberman (Brandeis) : Slice Knots and the Alexander PolynomialA knot in the 3-sphere is slice if it bounds an embedded disk in the 4-ball.The disk may be topologically embedded, or we may require the strongercondition that it be smoothly embedded, the knot is said to be (respectively)topologically or smoothly slice. It has been known since the early 1980's thatthere are knots that are topologically slice, but not smoothly slice. Theseresult from Freedman's proof that knots with trivial Alexander polynomial aretopologically slice, combined with gauge-theory techniques originating withDonaldson. In joint work with C. Livingston and M. Hedden, we show that thegroup of topologically slice knots, modulo those with trivial Alexanderpolynomial, is infinitely generated. The proof uses Heegaard-Floer theory, andalso applies to problems about link concordance. |
