Strongly minimal PD4-complexes

الأصل · EN

We consider the homotopy types of PD₄-complexes X with fundamental group π such that c.d.π=2 and π has one end. Let β=β₂(π;F₂) and w=w₁(X). Our main result is that (modulo two technical conditions on (π,w)) there are at most 2β orbits of k-invariants determining "strongly minimal" complexes (i.e., those with homotopy intersection pairing λₓ trivial). The homotopy type of a PD₄-complex X with π a PD₂-group is determined by π, w, λₓ and the v₂-type of X. Our result also implies that Fox's 2-knot with metabelian group is determined up to TOP isotopy and reflection by its group.