Knot concordance and homology cobordismReport as inadecuate



 Knot concordance and homology cobordism


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We consider the question: -If the zero-framed surgeries on two oriented knots in the 3-sphere are integral homology cobordant, preserving the homology class of the positive meridians, are the knots themselves concordant?- We show that this question has a negative answer in the smooth category, even for topologically slice knots. To show this we first prove that the zero-framed surgery on K is Z-homology cobordant to the zero-framed surgery on many of its winding number one satellites PK. Then we prove that in many cases the tau and s-invariants of K and PK differ. Consequently neither tau nor s is an invariant of the smooth homology cobordism class of the zero-framed surgery. We also show, that a natural rational version of this question has a negative answer in both the topological and smooth categories, by proving similar results for K and its p,1-cables.



Author: Tim D. Cochran; Bridget D. Franklin; Matthew Hedden; Peter D. Horn

Source: https://archive.org/







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