Mathematics – Geometric Topology
Scientific paper
2006-08-26
J. Math. Soc. Japan 58:4 (2006), 1151-1162
Mathematics
Geometric Topology
Scientific paper
The validity of Freedman's disk theorem is known to depend only on the fundamental group. It was conjectured that it fails for nonabelian free fundamental groups. If this were true then surgery theory would work in dimension four. Recently, Krushkal and Lee proved a surprising result that surgery theory works for a large special class of 4-manifolds with free nonabelian fundamental groups. The goal of this paper is to show that this also holds for other fundamental groups which are not known to be good, and that it is best understood using controlled surgery theory of Pedersen--Quinn--Ranicki. We consider some examples of 4-manifolds which have the fundamental group either of a closed aspherical surface or of a 3-dimensional knot space. A more general theorem is stated in the appendix.
Hegenbarth Friedrich
Repovš Dušan
No associations
LandOfFree
Applications of controlled surgery in dimension 4: Examples does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Applications of controlled surgery in dimension 4: Examples, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Applications of controlled surgery in dimension 4: Examples will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-43577