ALEXANDER DUALITY, GROPES AND LINK HOMOTOPY

VYACHESLAV S. KRUSHKAL AND PETER TEICHNER

Abstract. We prove a geometric refinement of Alexander duality for certain 2complexes, the so-called gropes, embedded into 4-space. 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 μ-invariants as in the original proofs.