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Title:
Shake concordance of knots (joint work with Tim Cochran)
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Abstract:
If $K$ is a knot in $S^3 = \partial B^4$, then the 4--manifold $W_K$ obtained by adding a single 2--handle to $S^3$ along $K$ with zero framing has $H_2(W_K) \cong \mathbb{Z}$. If a generator of $H_2(W_K)$ can be represented by an embedded sphere, $K$ is called \textit{shake-slice}. Any slice knot is shake-slice, but the converse is unknown. We define a relative version of this concept, known as \textit{shake-concordance}, and construct infinite families of knots that are pairwise shake-concordant but not concordant. We show that the concordance invariants $\tau$, $s$, and slice genus are not invariants of shake-concordance. We also give a characterization of shake-concordant and shake-slice knots in terms of concordance. (30 min long talk)
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