Title:  Some new 6-dimensional Hamiltonian S¹ manifolds.

Abstract:  I will construct some Hamiltonian S¹ manifolds M with H²(M)=Z
whose existence was first proposed by Sue Tolman.
The reduced spaces are one point orbifold blow ups of weighted
projective planes. The idea of the proof is to resolve the orbifold
singularities and so reduce the problem to one concerning the 7
or 8 point blow up of the projective plane. I will try to explain all
this in a very elementary way.