0000000000876648
AUTHOR
Michael H. Freedman
showing 2 related works from this author
4-Manifold topology I: Subexponential groups
1995
The technical lemma underlying the 5-dimensional topological s-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating ~-null immersions of disks. These conjectures are theorems precisely for those fundamental groups ("good groups") where the ~l-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 opera- tions: (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.
4-Manifold topology II: Dwyer's filtration and surgery kernels
1995
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.