Strongly minimal PD4-complexes

Jonathan A. Hillman


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 λX 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.

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Tuesday, October 23, 2007