Whitney towers and gropes in 4--manifolds

Details Whitney towers and gropes in 4--manifolds Whitney towers and gropes in 4--manifolds

2003-10-20

arxiv.org/abs/math/0310303v2

"Whitney towers and Gropes in 4--manifolds", Trans. Amer. Math. Soc. 358 (2006), 4251-4278

Mathematics

Geometric Topology

Now closely approximates published version. Some references added

Scientific paper

Many open problems and important theorems in low-dimensional topology have been formulated as statements about certain 2--complexes called gropes. This paper describes a precise correspondence between embedded gropes in 4--manifolds and the failure of the Whitney move in terms of iterated `towers' of Whitney disks. The `flexibility' of these Whitney towers is used to demonstrate some geometric consequences for knot and link concordance connected to n-solvability, k-cobordism and grope concordance. The key observation is that the essential structure of gropes and Whitney towers can be described by embedded unitrivalent trees which can be controlled during surgeries and Whitney moves.

Affiliated with

Also associated with

No associations

Rating

Whitney towers and gropes in 4--manifolds 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 Whitney towers and gropes in 4--manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Whitney towers and gropes in 4--manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-421182