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Invent math 122 531 557 1995 Inventiones mathematicae 9 Springer Verlag 1995 4 Manifold topology II Dwyer s filtration and surgery kernels Michael H Freedman j Peter Teichner 2 i University of California Department of Mathematics San Diego La lolla CA 92093 0112 USA e mail freedman euclid ucsd edu 2 Universitfit Mainz Fachbereich Mathematik D 55099 Mainz Germany e mail teichner topologie mathematik uni mainz de Oblatum 20 11 1995 26 V 1995 Abstract 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 o f 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 Introduction In dimension four the basic machinery of manifold theory surgery and 5 dimensional s cobordism theorems exist in the topological category when the fundamental group rr is good FT and is expected to fail for 7r free and nonabelian and in fact to fail for the random group Nevertheless even when rc is arbitrary many special surgery problems can profitably be solved The theorem F2 that the Whitehead double o f any boundary link is freely slice is an example These applications all involve some representation of the surgery kernel by a submanifold M whose inclusion M C N into the source o f the surgery problem is 7h null Whereas all previous applications IF2 F3 FQ Chapter 6 required the second homology of M to be spherical we find here see Theorem 1 1 and Corollary 1 2 that the important condition is only that H2 M bo M i e that the second homology lies in the co term of the Dwyer D filtration as discussed in Sect 2 This is an important philosophical point since for any n 1 the canonical or atomic compare CF



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