Alexander duality, gropes and link homotopy
几何拓扑
2014-11-11 v3
摘要
We prove a geometric refinement of Alexander duality for certain 2-complexes, the so-called gropes, embedded into 4-space. This refinement can be roughly formulated as saying that 4-dimensional Alexander duality preserves the disjoint Dwyer filtration. In addition, we give new proofs and extended versions of two lemmas of Freedman and Lin which are of central importance in the A-B-slice problem, the main open problem in the classification theory of topological 4-manifolds. Our methods are group theoretical, rather than using Massey products and Milnor \mu-invariants as in the original proofs.
引用
@article{arxiv.math/9705222,
title = {Alexander duality, gropes and link homotopy},
author = {Vyacheslav S. Krushkal and Peter Teichner},
journal= {arXiv preprint arXiv:math/9705222},
year = {2014}
}
备注
19 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper5.abs.html