Strongly minimal PD₄-complexes

Jonathan A. Hillman

Abstract

We consider the homotopy types of PD₄-complexes X with fundamental group π such that c.d.π=2 and π has one end. In particular, we show the homotopy type of a PD₄-complex X with π a PD₂-group is determined by π, w₁(X), the homotopy intersection pairing λ_X and the v₂-type of X. We show also that if m is even the closed orientable 4-manifold M with π₁(M)=Z*_m and χ(M)=0 is unique up to homeomorphism. This implies that Fox's 2-knot with metabelian group is determined up to TOP isotopy and reflection by its group.