On the topology of weighted projective spaces
Rider University, Lawrenceville NJ 08468, U.S.A.
This survey talk will be a review results obtained in collaboration with Mattias Franz and Nigel Ray. As singular toric varieties, weighted projective spaces have an action of a real torus. The equivariant cohomology with respect to this action is computed to be isomorphic to the ring of piecewise polynomials on the defining fan. The theory is seen to parallel that for smooth toric varieties with the role of the Stanley-Reisner ring replaced by the ring of piecewise polynomials. If time permits, an alternative presentation of weighted projective spaces as iterated Thom complexes will be discussed briefly. Further collaboration with Mattias Franz, Nigel Ray and Dietrich Notbohm yields in a complete topological classification of weighted projective spaces.