On the Quantum Cohomology of Fano Toric Manifolds and the Intersection Cohomology of Singular Symplectic Quotients

79 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999.The second result computes the intersection cohomology of the singular symplectic reduced spaces. Let M be a closed symplectic manifold with a Hamiltonian S1-action defined on it and mu is the moment map. If 0 is a singular value of mu, the reduced space mu-1(0)/S1 is, in general, no longer an orbifold but contains singularities. We show that there is a surjective map from the equivariant cohomology of M to the intersection cohomology of mu-1(0)/ S1. This result can be considered as a symplectic generalization of the Beilinson-Bernstein-Deligne-Gabor decomposition theorem for singular algebraic varieties. Using this surjectivity result and the localization technique, we can relate the pairings of the intersection cohomology classes to the equivariant cohomology classes in M. We show that a theorem of Kalkman has a direct generalization in the singular setting.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD