We review the basic definition of a stack and apply it to the topological and smooth settings. We then address two subtleties of the theory: the correct definition of a ``stack over a stack'' and the… Expand

It is well known that an effective orbifold M (one for which the local stabilizer groups act effectively) can be presented as a quotient of a smooth manifold P by a locally free action of a compact… Expand

We use symplectic cobordisrn, and the localization result of Ginzburg, Guillemin, and Karshon to find a wall-crossing formula for the signature of regular symplectic quotients of Hamiltonian torus… Expand

For an $S^{1}$-manifold with boundary, we prove a localization formula applying to any equivariant cohomology theory satisfying a certain algebraic condition. We show how the localization result of… Expand

In this thesis, we calculate various topological invariants of symplectic reduced spaces, also known as symplectic quotients. These invariants include the signature, the Poincar6 polynomial, and the… Expand

In an article in this MONTHLY in 1953 Metropolis and Ulam asked for the expected number of components of the graph induced by a purely random mapping of a set of n points into itself [7]. This… Expand

Abstract:We give a purely K-theoretic proof of a case of the “quantization commutes with reduction” result, conjectured by Guillemin and Sternberg and proved by Meinrenken and Vergne. We show that… Expand