4-manifold topology. II: Dwyer's filtration and surgery kernels
In the theory of 4-manifold topology, surgery and \(s\)-cobordism theorems hold, in the topological category, for the so-called good fundamental groups (including for example the elementary amenable groups and recently the subexponential groups as proved by the authors). Nevertheless, even when the fundamental group is arbitrary many special interesting 4-dimensional surgery problems can admit topological solutions. In general these results involve some representation of the surgery kernel by a submanifold \(M\) whose inclusion \(M\hookrightarrow N\) into the source of the surgery problem is \(\pi_1\)-null. In this fine paper, the authors unify and extend the known examples and find that the important condition to solve the 4-dimensional surgery problem is that the second homology group of \(M\) lies in the \(\omega\)-term of the Dwyer filtration [\textit{W. G. Dwyer}, J. Pure Appl. Algebra 6, 177-190 (1975; Zbl 0338.20057)]. As a consequence, a class of links, larger than boundary links and slightly smaller than homotopically trivial links, is proved to have free slices bounding their Whitehead doubles, and this extends previous results of the first author [Invent. Math. 80, 453-465 (1985; Zbl 0569.57002); 94, 175-182 (1988; Zbl 0678.57002)].
scientific article; zbMATH DE number 871779
scientific article