Filtering smooth concordance classes of topologically slice knots
A knot in \(S^3\) is topologically slice if it bounds a topologically embedded 2--disk in the 4--ball, \(B^4\), and is a slice knot if it bounds a smoothly embedded 2--disk. Refining and generalizing work by \textit{T. D. Cochran} and \textit{R. E. Gompf} [Topology 27, No.4, 495--512 (1988; Zbl 0669.57003)], the article introduces a new filtration of the topological knot concordance group that induces a non--trivial filtration \({\mathcal T}_n\) of the subgroup \({\mathcal T}\) of concordance classes of topological slice knots. The gauge--theoretic and \(\tau\), \(s\), \(\epsilon\)--invariants are shown to detect knots in \({\mathcal T}/{\mathcal T}_0\) while the \(d\)--invariants detect the non--triviality of \({\mathcal T}_0/{\mathcal T}_1\).
scientific article; zbMATH DE number 6198082
scientific article