Topology Seminar: Jonathan Hillman

In Section 11.5 of their book, Freedman and Quinn showed that an aspherical 4-manifold M with polycyclic fundamental group pi is determined by pi and the boundary of M. We revisit this result, with a shift in emphasis. We show that if Mis aspherical and pi is elementary amenable then pi is 1, ZZ, a Baumslag-Solitar group BS(1,m) or (torsion free) polycyclic of Hirsch length 3 or 4. We characterise the possible boundaries, except for the cases with pi=BS(1,m) for some m.

Joint work with Jim Davis, Bloomington.