Inventiones mathematicae

, Volume 122, Issue 1, pp 531–557 | Cite as

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

  • Michael H. Freedman
  • Peter Teichner
Article

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 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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References

  1. [CF] A. Casson, M.H. Freedman: Atomic surgery problems. Cont. Math.35, 181–199 (1984)Google Scholar
  2. [C] T. Cochran: Derivative's of links: Milnor's Concordance invariants and Massey products, Vol.84, # 427, Memoirs of the A.M.S., Providence, Rhode Island, 1990Google Scholar
  3. [D] W. Dwyer: Homology, Massey products and maps between groups. J. Pure Appl. Algebra6, 177–190 (1975)Google Scholar
  4. [F1] M.H. Freedman: The topology of 4-dimensional manifolds. J. Diff. Geom.17, 357–453 (1982)Google Scholar
  5. [F2] M.H. Freedman: A new technique for the link slice problem. Invent. Math.80, 453–465 (1985)Google Scholar
  6. [F3] M.H. Freedman, Whitehead3 is a slice link. Invent. Math.94, 175–182 (1988)Google Scholar
  7. [FQ] M.H. Freedman, F. Quinn: The topology of 4-manifolds. Princeton Math. Series 39, Princeton, NJ, 1990Google Scholar
  8. [FT] M.H. Freedman, P. Teichner: 4-Manifold Topology I: Subexponential Groups (to appear)Google Scholar
  9. [K] Kojima: Milnor's\(\bar \mu \)-invariants, Massey products and Whitney's trick in 4 dimensions. Top. Appl.16, 43–60 (1983)Google Scholar
  10. [K] X.S. Lin: On equivalence relations of links in 3-manifolds. Preprint (1985)Google Scholar
  11. [MKS] W. Magnus, A. Karras, D. Solitar. Combinatorial group theory. Dover Publications, New York, 1966Google Scholar
  12. [M1] J. Milnor: Link Groups. Ann. Math.59, 177–195 (1954)Google Scholar
  13. [M2] J. Milnor: Isotopy of links, Algebraic geometry and Topology. Princeton Univ. Press, pp. 280–306, 1957Google Scholar
  14. [St] J. Stallings: Homology and central series of groups. J. Algebra2, 1970–1981 (1965)Google Scholar
  15. [T] V.G. Turaev: Milnor's invariants and Massey products, Studies in topology II. Zap. Nauc. Sem Leningrad (LOMI)66, 189–203, 209–210 (1976)Google Scholar
  16. [V] M. Vaughan-Lee: The restricted Burnside problem. London Math. Soc. Monographs New Series 8, Clarendon Press, 1993Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Michael H. Freedman
    • 1
  • Peter Teichner
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaSan Diego, La JollaUSA
  2. 2.Fachbereich MathematikUniversität MainzMainzGermany

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