Inventiones mathematicae

, Volume 122, Issue 1, pp 509–529 | Cite as

4-Manifold topology I: Subexponential groups

  • Michael H. Freedman
  • Peter Teichner


The technical lemma underlying the 5-dimensional topologicals-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating π1-null immersions of disks. These conjectures are theorems precisely for those fundamental groups (“good groups”) where the π1-null disk lemma (NDL) holds. We expand the class of known good groups to all groups of subexponential growth and those that can be formed from these by a finite number of application of two operations: (1) extension and (2) direct limit. The finitely generated groups in this class are amenable and no amenable group is known to lie outside this class.


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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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