On the algebraic topology of weighted projective spaces

From the viewpoint of algebraic topology, a quasitoric orbifold is a singular space that is constructed out of a simple polytope and a related integral matrix, and admits a well-behaved torus action. Weighted projective spaces P(χ) provide a particularly illuminating class of examples (where χ denotes a weight vector of natural numbers), but their topological literature is remarkably sparse. Our aim would be to introduce an audience of geometers to some of the more fundamental topological properties of P(χ), based on recent and ongoing work with Tony Bahri and Matthias Franz. We would expect to describe their integral cohomology rings, both ordinary and equivariant, in terms of piecewise polynomials, and to sketch relationships between P(χ) and the Borel construction, homotopy colimits, and iterated Thom complexes.