, Volume 122, Issue 1, pp 531-557

4-Manifold topology II: Dwyer's filtration and surgery kernels

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Even when the fundamental group is intractable (i.e. not “good”) many interesting 4-dimensional surgery problems have topological solutions. We unify and extend the known examples and show how they compare to the (presumed) counterexamples by reference to Dwyer's filtration on second homology. The development brings together many basic results on the nilpotent theory of links. As a special case, a class of links only slightly smaller than “homotopically trivial links” is shown to have (free) slices on their Whitehead doubles.

Oblatum 20-II-1995 & 26-V-1995
The first author is supported by the IHES, the Guggenheim foundation and the NSF.
The second author is supported by the IHES and the Humboldt foundation.