Exotic Mazur manifolds exist, and the knot Floer invariant ν is shown to be an invariant of knot traces, yielding counterexamples to a conjecture in Kirby's problem list.
The Conway knot is not slice
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abstract
A knot is said to be slice if it bounds a smooth properly embedded disk in the 4-ball. We demonstrate that the Conway knot, 11n34 in the Rolfsen tables, is not slice. This completes the classification of slice knots under 13 crossings, and gives the first example of a non-slice knot which is both topologically slice and a positive mutant of a slice knot.
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Exotic Mazur manifolds and knot trace invariants
Exotic Mazur manifolds exist, and the knot Floer invariant ν is shown to be an invariant of knot traces, yielding counterexamples to a conjecture in Kirby's problem list.