A counterexample to the strong version of Freedman's conjecture

Details A counterexample to the strong version of Freedman's conjecture A counterexample to the strong version of Freedman's conjecture

2006-10-27

arxiv.org/abs/math/0610865v2

Ann. of Math. 168 (2008), 675-693

Mathematics

Geometric Topology

20 pages

Scientific paper

A long-standing conjecture due to Michael Freedman asserts that the 4-dimensional topological surgery conjecture fails for non-abelian free groups, or equivalently that a family of canonical examples of links (the generalized Borromean rings) are not A-B slice. A stronger version of the conjecture, that the Borromean rings are not even weakly A-B slice, where one drops the equivariant aspect of the problem, has been the main focus in search for an obstruction to surgery. We show that the Borromean rings, and more generally all links with trivial linking numbers, are in fact weakly A-B slice. This result shows the lack of a non-abelian extension of Alexander duality in dimension 4, and of an analogue of Milnor's theory of link homotopy for general decompositions of the 4-ball.

Affiliated with

Also associated with

No associations

Rating

A counterexample to the strong version of Freedman's conjecture 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 A counterexample to the strong version of Freedman's conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A counterexample to the strong version of Freedman's conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-448379