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4:00 pm Monday, October 28, 2013 Topology Seminar: Shake concordant knots that are not concordantby Tim Cochran (Rice) in HB 427- If K is a knot in the boundary of a 4-ball, then the 4-manifold W(K,0) obtained from the 4-ball by adding a single two-handle along K with framing zero, has H_2=Z. The shake genus of K is the minimum genus of an embedded surface representing a generator of H_2. The question was asked whether the shake genus is equal to the slice genus of K. In particular if the shake genus is zero then the knot is called shake slice. Then the question becomes: is every shake slice knot a slice knot? There has been no progress on this question since 1976. We answer , in the negative, a relative version of this question. This is joint work with Aru Ray.
Submitted by cochran@rice.edu |