Inventiones mathematicae

, Volume 122, Issue 1, pp 531–557

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


  • Michael H. Freedman
    • Department of MathematicsUniversity of California
  • Peter Teichner
    • Fachbereich MathematikUniversität Mainz

DOI: 10.1007/BF01231455

Cite this article as:
Freedman, M.H. & Teichner, P. Invent Math (1995) 122: 531. doi:10.1007/BF01231455


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.

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© Springer-Verlag 1995