In the 60's Levine proved that if is a slice knot, then on any genus Seifert surface for there is a component link , called a derivative of , on which the Seifert form vanishes. Many subsequent obstructions to being slice are given in terms of slice obstructions of . Many of these obstructi…
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The study shows that positive scalar curvature 4-manifolds can be desingularized.
problem Proving the non-existence of singular positive scalar curvature metrics.
method Explicit constructions from scalar-flat Kähler ALE surfaces and desingularization process.
result Desingularization of positive scalar curvature 4-manifolds is possible.
We define a set of "second-order" L^(2)-signature invariants for any algebraically slice knot. These obstruct a knot's being a slice knot and generalize Casson-Gordon invariants, which we consider to be "first-order signatures". As one application we prove: If K is a genus one slice knot then, on any genus one Seifert …